CN102916802B - Fractional-order automatic switching chaotic system method for four Lorenz type systems and analog circuit - Google Patents

Abstract

The invention discloses a method and an analog circuit for automatically switching chaotic systems based on the fractional order four systems of the Lorenz type system. , multiplier U9, multiplier U10, voltage comparator U7, and analog switch U6. The present invention utilizes analog circuits to realize a fractional-order chaotic system that automatically switches four Lorenz-type subsystems, compared to a system composed of two or three sub-chaotic systems. Automatic switching chaotic systems and non-switching fractional chaotic systems are more complex and more random, and can become a new choice of signal source for secure communication, and have better application prospects in secure communication.

Description

Chaotic system method and analog circuit for automatic switching of four systems of fractional order based on Lorenz type system

technical field

The invention relates to a method for automatically switching chaotic systems based on a Lorenz-type system of four systems of fractional order, in particular to a method and an analog circuit for automatically switching chaotic systems of four systems of fractional order based on a Lorenz-type system.

Background technique

At present, there are many ways to use analog circuits to realize integer-order and fractional-order chaotic systems and circuits, but there are relatively few methods for using analog circuits to realize automatic switching chaotic circuits, and the disclosed automatic switching chaotic systems and circuits are integer order 2 There is no disclosure of a method and circuit for automatic switching of multiple sub-chaotic systems. The present invention provides a method and an analog circuit for automatically switching chaotic systems of four Lorenz-type fractional systems, which enriches the automatic switching of chaotic systems. The number and type of , improve the randomness of the chaotic system, and have a good application prospect in secure communication.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method and an analog circuit for automatically switching chaotic systems of four systems of fractional order based on the Lorenz type system.

The present invention adopts following technical means to realize the object of the invention:

1. The method for automatically switching the chaotic system based on the fractional order four systems of the Lorenz type system is characterized in that, comprising the following steps:

(1) According to the Lorenz type chaotic system I is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|x\right|-\mathrm{hz}\end{array}\right.---I$ a=20, b=14, c=10.6, h=2.8

(2) According to the Lorenz type chaotic system II:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|\mathrm{the\; y}\right|-\mathrm{hz}\end{array}\right.---\mathrm{II}$ a=20, b=14, c=10.6, h=2.8

(3) According to the chaotic system, the symbolic functions III and IV are constructed as:

$\mathrm{<span\; class="notranslate">\; sign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; III</span>}$

$\mathrm{<span\; class="notranslate">\; sign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; IV</span>}$

(4) According to the Lorenz type chaotic system V is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xsign}\left(\mathrm{the\; y}\right)-\mathrm{hz}\end{array}\right.---V$ a=20, b=14, c=10.6, h=2.8

(5) According to Lorenz type chaotic system VI is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{ysign}\left(x\right)-\mathrm{hz}\end{array}\right.---\mathrm{VI}$ a=20, b=14, c=10.6, h=2.8

(6) According to the construction of the chaotic system, the selection function VII is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; xy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; xsign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; ysign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; |</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; VII</span>}$

(7) According to system I, II, V, VI and selection function VII, construct a Lorenz-type four-system automatic switching chaotic system IX

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---\mathrm{IX}$ a=20, b=14, c=10.6, h=2.8

(8) Construct a Lorenz-type fractional-order four-system automatic switching chaotic system X according to system IX

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(\mathrm{the\; y}-x)\\ d^q\mathrm{the\; y}/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---x$ 0<q<1, a=20, b=14, c=10.6, h=2.8

(9) Construct analog circuit system according to chaotic system X, utilize voltage comparator U7 to obtain two analog high and low levels, x>=0 or x<0 and y>=0 or y<0, as the control of analog switch U6 Input, according to four different situations of x>=0, y>=0, x>=0, y<0, x<0, y>=0 and x<0, y<0, realize the difference of f(xy) Output, so as to realize the chaotic system IX of automatic switching of four systems, and then realize the chaotic system X through fractional order integration, operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 adopt LF347, multiplier U4, The multiplier U9 and multiplier U10 use AD633JN, the analog switch U6 uses ADG409, and the voltage comparator U7 uses LM139;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, connected to the sixth pin through the resistor R1, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of the resistor Rc11 and the capacitor C11, then connected to the parallel connection of the resistor Rc12 and the capacitor C12, and then connected to the parallel connection of the resistor Rc13 and the capacitor C13 Then connect to the 7th pin, the 7th pin is connected to the 13th pin through the resistor R13, the 2nd pin of U2 is connected to the potentiometer R22, the 1st pin of U4 is connected, and the 2nd pin of U5 is connected to the resistor Ra1 , connected to the 5th pin of U7, connected to the 2nd pin of U8, connected to the 1st pin of U9, the 8th pin is connected to the 9th pin through the resistor R25, and the 13th pin is connected to the 14th pin through the resistor R14 , the 14th pin is connected to the 2nd pin through the potentiometer R11;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, connected to the sixth pin through the resistor R2, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of resistor Rc21 and capacitor C21, then connected to the parallel connection of Rc22 and capacitor C22, and then connected to the parallel connection of Rc23 and capacitor C23 The 7th pin, the 7th pin is connected to the 2nd pin through the potentiometer R23, the 9th pin of U1 is connected through the resistor R24, the 2nd pin of U1 is connected through the potentiometer R12, and the 13th pin of U5 is connected through Ra6 Pin, connected to the 11th pin of U7, connected to the 13th pin of U8, connected to the 1st pin of U10, the 8th pin connected to the 13th pin through the resistor R33, first connected to the parallel connection of Rc31 and capacitor C31, and then Connect the parallel connection of Rc32 and capacitor C32, and connect the parallel connection of resistor Rc33 and capacitor C33 to the 9th pin, the 13th pin is connected to the 14th pin through the resistor R34, and the 14th pin is connected to the 2nd pin of U3 through the potentiometer R32 Pin, connected to the third pin of U4;

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, the ninth pin of U2 is connected through the resistor R3, the second pin of U3 is connected to the 14th pin of U2 through R32, and the third pin The pin is grounded, the 4th pin is connected to VCC, the 5th pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 10th pin, the 12th pin, the 13th pin, The 14th pin is suspended, and the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the seventh pin of U1, the third pin is connected to the fourteenth pin of U2, the second, fourth, and sixth pins are all grounded, the fifth pin is connected to VEE, and the seventh pin is connected to VEE. The pin is connected to the second pin of U2 through the potentiometer R21, and the eighth pin is connected to VCC;

The first pin of the operational amplifier U5 is connected to the second pin through the diode D3, the second pin is connected to the seventh pin of U1 through the resistor Ra1, the first pin is connected in series through the resistor Ra2 and the diode D4, and the resistor The series connection of Ra1 and resistor Ra5 is connected to the 6th pin, the series connection of the resistors Ra2 and Ra3 is connected to the 6th pin, the 3rd pin, the 5th pin, the 10th pin, the 12th pin are grounded, and the 4th pin Connect to the positive 14V power supply, connect the 11th pin to the negative 14V power supply, connect the 6th pin to the 7th pin through the resistor Ra4, connect the 7th pin to the 7th pin of U6, and connect the 8th pin to the 5th pin of U6 , connected to the 9th pin through the resistor Ra9, the 9th pin is connected to the 14th pin through the series connection of the resistor Ra8 and the diode D6, connected to the 13th pin through the series connection of the resistor Ra10 and Ra6, and the 13th pin is connected to the 13th pin through the resistor Ra7 and the diode The series of D6 is connected to the 14th pin, and the 14th pin is connected to the 13th pin through the diode D5;

The first pin of the analog switch U6 is connected to the second pin of U7, the second pin and the fourteenth pin are connected to the positive 14V power supply, the third pin is connected to the negative 14V power supply, and the fourth pin is connected to the seventh pin of U10. pin, the 5th pin is connected to the 8th pin of U5, the 6th pin is connected to the 7th pin of U9, the 7th pin is connected to the 7th pin of U5, and the 8th pin is connected to the U3 through the potentiometer R31 The 2nd pin, the 9th pin, the 10th pin, the 11th pin, the 12th pin, the 13th pin is floating, the 15th pin is grounded, the 16th pin is connected to the 13th pin of U7;

The 1st pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, and the 14th pin of the voltage comparator U7 are suspended, the 3rd pin is connected to VCC, the 4th pin, The 10th pin and the 12th pin are grounded, the 2nd pin is connected to the positive 14V power supply through the resistor R01, and grounded through the series connection of the diode D1 and the resistor R02, the 13th pin is connected to the positive 14V power supply through the resistor R03, through the diode D2 and the resistor R04 series grounding;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rs1, the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, and the twelfth pin Ground, the 4th pin is connected to the positive 14V power supply, the 11th pin is connected to the negative 14V power supply, the 6th pin is connected to the 7th pin through the resistor Rs2, the 7th pin is connected to the 3rd pin of U10, and the 8th pin is connected to The 3rd pin of U9 is connected to the 9th pin through RS4, the 9th pin is connected to the 14th pin through the resistor Rs3, and the 13th pin is connected to the 7th pin of U2;

The 1st pin of described multiplier U9 connects the 7th pin of U1, the 3rd pin connects the 8th pin of U8, the 2nd pin, the 4th pin, the 6th pin are grounded, the 5th pin Connect to VEE, connect the 7th pin to the 6th pin of U6, and connect the 8th pin to VCC;

The first pin of the multiplier U10 is connected to the seventh pin of U2, the third pin is connected to the seventh pin of U8, the second pin, the fourth pin, and the sixth pin are grounded, and the fifth pin Connect to VEE, connect the 7th pin to the 4th pin of U6, and connect the 8th pin to VCC.

2, based on the fractional order four systems of the Lorenz type system, the automatic switching analog circuit is characterized in that the operational amplifier U1, the operational amplifier U2, the operational amplifier U3, the operational amplifier U5, the operational amplifier U8 and the multiplier U4 and the multiplier U9 , multiplier U10, voltage comparator U7 and analog switch U6, the operational amplifier U1 is connected to the voltage comparator U7, operational amplifier U5, operational amplifier U8, multiplier U4, operational amplifier U2, and the operational amplifier U2 is connected to the operational amplifier U1, an operational amplifier U5, a voltage comparator U7, and an operational amplifier U8, the operational amplifier U3 is connected to the operational amplifier U2 and the multiplier U4, the operational amplifier U5 is connected to the analog switch U6, and the voltage comparator U7 is connected to the analog switch U6, The operational amplifier U8 is connected to the operational amplifier U5, the multiplier U9, and the multiplier U10, the multiplier U9 is connected to the analog switch U6, and the multiplier U10 is connected to the analog switch U6;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, connected to the sixth pin through the resistor R1, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of the resistor Rc11 and the capacitor C11, then connected to the parallel connection of the resistor Rc12 and the capacitor C12, and then connected to the parallel connection of the resistor Rc13 and the capacitor C13 Then connect to the 7th pin, the 7th pin is connected to the 13th pin through the resistor R13, the 2nd pin of U2 is connected to the potentiometer R22, the 1st pin of U4 is connected, and the 2nd pin of U5 is connected to the resistor Ra1 , connected to the 5th pin of U7, connected to the 2nd pin of U8, connected to the 1st pin of U9, the 8th pin is connected to the 9th pin through the resistor R25, and the 13th pin is connected to the 14th pin through the resistor R14 , the 14th pin is connected to the 2nd pin through the potentiometer R11;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, connected to the sixth pin through the resistor R2, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of resistor Rc21 and capacitor C21, then connected to the parallel connection of Rc22 and capacitor C22, and then connected to the parallel connection of Rc23 and capacitor C23 The 7th pin, the 7th pin is connected to the 2nd pin through the potentiometer R23, the 9th pin of U1 is connected through the resistor R24, the 2nd pin of U1 is connected through the potentiometer R12, and the 13th pin of U5 is connected through Ra6 Pin, connected to the 11th pin of U7, connected to the 13th pin of U8, connected to the 1st pin of U10, the 8th pin connected to the 13th pin through the resistor R33, first connected to the parallel connection of Rc31 and capacitor C31, and then Connect the parallel connection of Rc32 and capacitor C32, and connect the parallel connection of resistor Rc33 and capacitor C33 to the 9th pin, the 13th pin is connected to the 14th pin through the resistor R34, and the 14th pin is connected to the 2nd pin of U3 through the potentiometer R32 Pin, connected to the third pin of U4;

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, the ninth pin of U2 is connected through the resistor R3, the second pin of U3 is connected to the 14th pin of U2 through R32, and the third pin The pin is grounded, the 4th pin is connected to VCC, the 5th pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 10th pin, the 12th pin, the 13th pin, The 14th pin is suspended, and the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the seventh pin of U1, the third pin is connected to the fourteenth pin of U2, the second, fourth, and sixth pins are all grounded, the fifth pin is connected to VEE, and the seventh pin is connected to VEE. The pin is connected to the second pin of U2 through the potentiometer R21, and the eighth pin is connected to VCC;

The first pin of the operational amplifier U5 is connected to the second pin through the diode D3, the second pin is connected to the seventh pin of U1 through the resistor Ra1, the first pin is connected in series through the resistor Ra2 and the diode D4, and the resistor The series connection of Ra1 and resistor Ra5 is connected to the 6th pin, the series connection of the resistors Ra2 and Ra3 is connected to the 6th pin, the 3rd pin, the 5th pin, the 10th pin, the 12th pin are grounded, and the 4th pin Connect to the positive 14V power supply, connect the 11th pin to the negative 14V power supply, connect the 6th pin to the 7th pin through the resistor Ra4, connect the 7th pin to the 7th pin of U6, and connect the 8th pin to the 5th pin of U6 , connect to the 9th pin through the resistor Ra9, connect the 9th pin to the 14th pin through the series connection of the resistor Ra8 and the diode D6, connect the 13th pin through the series connection of the resistor Ra10 and Ra6, connect the 13th pin through the series connection of the resistor Ra7 and the diode D6 14 pins, the 14th pin is connected to the 13th pin through the diode D5;

The first pin of the analog switch U6 is connected to the second pin of U7, the second pin and the fourteenth pin are connected to the positive 14V power supply, the third pin is connected to the negative 14V power supply, and the fourth pin is connected to the seventh pin of U10. pin, the 5th pin is connected to the 8th pin of U5, the 6th pin is connected to the 7th pin of U9, the 7th pin is connected to the 7th pin of U5, and the 8th pin is connected to the U3 through the potentiometer R31 The 2nd pin, the 9th pin, the 10th pin, the 11th pin, the 12th pin, the 13th pin is floating, the 15th pin is grounded, the 16th pin is connected to the 13th pin of U7;

The 1st pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, and the 14th pin of the voltage comparator U7 are suspended, the 3rd pin is connected to VCC, the 4th pin, The 10th pin and the 12th pin are grounded; the 2nd pin is connected to the positive 14V power supply through the resistor R01, and grounded through the series connection of the diode D1 and the resistor R02; the 13th pin is connected to the positive 14V power supply through the resistor R03, and the diode D2 and the resistor R04 series grounding;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rs1, the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, and the twelfth pin Ground, the 4th pin is connected to the positive 14V power supply, the 11th pin is connected to the negative 14V power supply, the 6th pin is connected to the 7th pin through the resistor Rs2, the 7th pin is connected to the 3rd pin of U10, and the 8th pin is connected to The 3rd pin of U9 is connected to the 9th pin through RS4, the 9th pin is connected to the 14th pin through the resistor Rs3, and the 13th pin is connected to the 7th pin of U2;

The 1st pin of described multiplier U9 connects the 7th pin of U1, the 3rd pin connects the 8th pin of U8, the 2nd pin, the 4th pin, the 6th pin are grounded, the 5th pin Connect to VEE, connect the 7th pin to the 6th pin of U6, and connect the 8th pin to VCC;

The first pin of the multiplier U10 is connected to the seventh pin of U2, the third pin is connected to the seventh pin of U8, the second pin, the fourth pin, and the sixth pin are grounded, and the fifth pin Connect to VEE, connect the 7th pin to the 4th pin of U6, and connect the 8th pin to VCC.

Description of drawings

FIG. 1 is a schematic diagram of a circuit connection structure of a preferred embodiment of the present invention.

FIG. 2 is a schematic diagram of the peripheral circuit structure of the operational amplifier U1.

FIG. 3 is a schematic structural diagram of the peripheral circuit of the operational amplifier U2 and the multiplier U4.

FIG. 4 is a schematic diagram of the peripheral circuit structure of the operational amplifier U5.

FIG. 5 is a schematic structural diagram of the peripheral circuits of the operational amplifier U8, the multiplier U9 and the multiplier U10.

FIG. 6 is a schematic diagram of the peripheral circuit structure of the operational amplifier U3, the voltage comparator U7 and the analog switch U6.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and preferred embodiments.

Referring to Fig. 1-Fig. 6, at first construct Lorenz type fractional order four systems automatic switching chaotic system, the system selected in this preferred embodiment

(1) According to the Lorenz type chaotic system I is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|x\right|-\mathrm{hz}\end{array}\right.---I$ a=20, b=14, c=10.6, h=2.8

(2) According to the Lorenz type chaotic system II:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|\mathrm{the\; y}\right|-\mathrm{hz}\end{array}\right.---\mathrm{II}$ a=20, b=14, c=10.6, h=2.8

(3) According to the chaotic system, the symbolic functions III and IV are constructed as:

$\mathrm{<span\; class="notranslate">\; sign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; III</span>}$

$\mathrm{<span\; class="notranslate">\; sign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; IV</span>}$

(4) According to the Lorenz type chaotic system V is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xsign}\left(\mathrm{the\; y}\right)-\mathrm{hz}\end{array}\right.---V$ a=20, b=14, c=10.6, h=2.8

(5) According to Lorenz type chaotic system VI is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{ysign}\left(x\right)-\mathrm{hz}\end{array}\right.---\mathrm{VI}$ a=20, b=14, c=10.6, h=2.8

(6) According to the construction of the chaotic system, the selection function VII is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; xy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; xsign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; ysign</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; |</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; VII</span>}$

(7) According to system I, II, V, VI and selection function VII, construct a Lorenz-type four-system automatic switching chaotic system IX

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(\mathrm{the\; y}-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---\mathrm{IX}$ a=20, b=14, c=10.6, h=2.8

(8) Construct a Lorenz-type fractional-order four-system automatic switching chaotic system X according to system IX

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(\mathrm{the\; y}-x)\\ d^q\mathrm{the\; y}/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---x$ 0<q<1, a=20, b=14, c=10.6, h=2.8

(9) Construct analog circuit system according to chaotic system X, utilize voltage comparator U7 to obtain two analog high and low levels, x>=0 or x<0 and y>=0 or y<0, as the control of analog switch U6 Input, according to four different situations of x>=0, y>=0, x>=0, y<0, x<0, y>=0 and x<0, y<0, realize the difference of f(xy) Output, so as to realize the chaotic system IX of automatic switching of four systems, and then realize the chaotic system X through fractional order integration, operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 adopt LF347, multiplier U4, The multiplier U9 and multiplier U10 use AD633JN, the analog switch U6 uses ADG409, and the voltage comparator U7 uses LM139;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, connected to the sixth pin through the resistor R1, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of the resistor Rc11 and the capacitor C11, then connected to the parallel connection of the resistor Rc12 and the capacitor C12, and then connected to the parallel connection of the resistor Rc13 and the capacitor C13 Then connect to the 7th pin, the 7th pin is connected to the 13th pin through the resistor R13, the 2nd pin of U2 is connected to the potentiometer R22, the 1st pin of U4 is connected, and the 2nd pin of U5 is connected to the resistor Ra1 , connected to the 5th pin of U7, connected to the 2nd pin of U8, connected to the 1st pin of U9, the 8th pin is connected to the 9th pin through the resistor R25, and the 13th pin is connected to the 14th pin through the resistor R14 , the 14th pin is connected to the 2nd pin through the potentiometer R11;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, connected to the sixth pin through the resistor R2, the third pin, the fifth pin, the tenth pin, and the twelfth pin The pin is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is first connected to the parallel connection of resistor Rc21 and capacitor C21, then connected to the parallel connection of Rc22 and capacitor C22, and then connected to the parallel connection of Rc23 and capacitor C23 The 7th pin, the 7th pin is connected to the 2nd pin through the potentiometer R23, the 9th pin of U1 is connected through the resistor R24, the 2nd pin of U1 is connected through the potentiometer R12, and the 13th pin of U5 is connected through Ra6 Pin, connected to the 11th pin of U7, connected to the 13th pin of U8, connected to the 1st pin of U10, the 8th pin connected to the 13th pin through the resistor R33, first connected to the parallel connection of Rc31 and capacitor C31, and then Connect the parallel connection of Rc32 and capacitor C32, and connect the parallel connection of resistor Rc33 and capacitor C33 to the 9th pin, the 13th pin is connected to the 14th pin through the resistor R34, and the 14th pin is connected to the 2nd pin of U3 through the potentiometer R32 Pin, connected to the third pin of U4;

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, the ninth pin of U2 is connected through the resistor R3, the second pin of U3 is connected to the 14th pin of U2 through R32, and the third pin The pin is grounded, the 4th pin is connected to VCC, the 5th pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 10th pin, the 12th pin, the 13th pin, The 14th pin is suspended, and the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the seventh pin of U1, the third pin is connected to the fourteenth pin of U2, the second, fourth, and sixth pins are all grounded, the fifth pin is connected to VEE, and the seventh pin is connected to VEE. The pin is connected to the second pin of U2 through the potentiometer R21, and the eighth pin is connected to VCC;

The first pin of the operational amplifier U5 is connected to the second pin through the diode D3, the second pin is connected to the seventh pin of U1 through the resistor Ra1, the first pin is connected in series through the resistor Ra2 and the diode D4, and the resistor The series connection of Ra1 and resistor Ra5 is connected to the 6th pin, the series connection of the resistors Ra2 and Ra3 is connected to the 6th pin, the 3rd pin, the 5th pin, the 10th pin, the 12th pin are grounded, and the 4th pin Connect to the positive 14V power supply, connect the 11th pin to the negative 14V power supply, connect the 6th pin to the 7th pin through the resistor Ra4, connect the 7th pin to the 7th pin of U6, and connect the 8th pin to the 5th pin of U6 , connected to the 9th pin through the resistor Ra9, the 9th pin is connected to the 14th pin through the series connection of the resistor Ra8 and the diode D6, connected to the 13th pin through the series connection of the resistor Ra10 and Ra6, and the 13th pin is connected to the 13th pin through the resistor Ra7 and the diode The series of D6 is connected to the 14th pin, and the 14th pin is connected to the 13th pin through the diode D5;

The first pin of the analog switch U6 is connected to the second pin of U7, the second pin and the fourteenth pin are connected to the positive 14V power supply, the third pin is connected to the negative 14V power supply, and the fourth pin is connected to the seventh pin of U10. pin, the 5th pin is connected to the 8th pin of U5, the 6th pin is connected to the 7th pin of U9, the 7th pin is connected to the 7th pin of U5, and the 8th pin is connected to the U3 through the potentiometer R31 The 2nd pin, the 9th pin, the 10th pin, the 11th pin, the 12th pin, the 13th pin is floating, the 15th pin is grounded, the 16th pin is connected to the 13th pin of U7;

The 1st pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, and the 14th pin of the voltage comparator U7 are suspended, the 3rd pin is connected to VCC, the 4th pin, The 10th pin and the 12th pin are grounded, the 2nd pin is connected to the positive 14V power supply through the resistor R01, and grounded through the series connection of the diode D1 and the resistor R02, the 13th pin is connected to the positive 14V power supply through the resistor R03, through the diode D2 and the resistor R04 series grounding;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rs1, the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, and the twelfth pin Ground, the 4th pin is connected to the positive 14V power supply, the 11th pin is connected to the negative 14V power supply, the 6th pin is connected to the 7th pin through the resistor Rs2, the 7th pin is connected to the 3rd pin of U10, and the 8th pin is connected to The 3rd pin of U9 is connected to the 9th pin through RS4, the 9th pin is connected to the 14th pin through the resistor Rs3, and the 13th pin is connected to the 7th pin of U2;

The 1st pin of described multiplier U9 connects the 7th pin of U1, the 3rd pin connects the 8th pin of U8, the 2nd pin, the 4th pin, the 6th pin are grounded, the 5th pin Connect to VEE, connect the 7th pin to the 6th pin of U6, and connect the 8th pin to VCC;

The first pin of the multiplier U10 is connected to the seventh pin of U2, the third pin is connected to the seventh pin of U8, the second pin, the fourth pin, and the sixth pin are grounded, and the fifth pin Connect to VEE, connect the 7th pin to the 4th pin of U6, and connect the 8th pin to VCC.

Of course, the above description is not a limitation to the invention, and the present invention is not limited to the above examples, and the changes, modifications, additions or replacements made by those skilled in the art within the scope of the present invention also belong to the scope of the present invention. protected range.

Claims (2)

1., based on the method for the fractional order four systems automatically switched chaotic system of Lorenz type system, it is characterized in that being, comprise the following steps:

(1) according to Lorenz type chaos system I be:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|x\right|-\mathrm{hz}\end{array}\right.---I$ a＝20,b＝14,c＝10.6,h＝2.8

(2) according to Lorenz type chaos system II be:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\left|x\right|-\mathrm{hz}\end{array}\right.---\mathrm{II}$ a＝20,b＝14,c＝10.6,h＝2.8

(3) according to chaos system structure sign function III and IV be:

$\mathrm{sign}\left(x\right)=\left\{\begin{array}{cc}1& x\&GreaterEqual;0\\ -1& x<0\end{array}\right.---\mathrm{III}$

$\mathrm{sign}\left(y\right)=\left\{\begin{array}{cc}1& y\&GreaterEqual;0\\ -1& y<0\end{array}\right.---\mathrm{IV}$

(4) according to Lorenz type chaos system V be:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xsign}\left(y\right)-\mathrm{hz}\end{array}\right.---V$ a＝20,b＝14,c＝10.6,h＝2.8

(5) according to Lorenz type chaos system VI be:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{ysign}\left(x\right)-\mathrm{hz}\end{array}\right.---\mathrm{VI}$ a＝20,b＝14,c＝10.6,h＝2.8

(6) according to chaos system structure choice function VII be:

$f\left(\mathrm{xy}\right)=\left\{\begin{array}{cc}\left|x\right|& x\&GreaterEqual;0,y\&GreaterEqual;0\\ \mathrm{xsign}\left(y\right)& x\&GreaterEqual;0,y<0\\ \mathrm{ysign}\left(x\right)& x<0,y\&GreaterEqual;0\\ \left|y\right|& x<0,y<0\end{array}\right.---\mathrm{VII}$

(7) a Lorenz type four systems automatically switched chaotic system IX is constructed according to system I, II, V, VI and choice function VII

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---\mathrm{IX}$ a＝20,b＝14,c＝10.6,h＝2.8

(8) a Lorenz type fractional order four systems automatically switched chaotic system X is constructed according to system IX

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(y-x)\\ d^{q}y/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=f\left(\mathrm{xy}\right)-\mathrm{hz}\end{array}\right.---X$ 0<q<1,a＝20,b＝14,c＝10.6,h＝2.8

(9) according to chaos system X constructing analog Circuits System, voltage comparator U7 is utilized to obtain the low and high level of two simulations, x>=0 or x<0 and y>=0 or y<0, as the control inputs of analog switch U6, according to x>=0, y>=0, x>=0, y<0, x<0, y>=0 and x<0, y<0 tetra-kinds of different situations, the difference realizing f (xy) exports, thus realize the chaos system IX of four systems automatic switchover, chaos system X is realized again by fractional order integration, operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 adopts LF347, multiplier U4, multiplier U9, multiplier U10 adopts AD633JN, analog switch U6 adopts ADG409, voltage comparator U7 adopts LM139,

1st pin of described operational amplifier U1 is connected with the 2nd pin by resistance Rx, connected with the 6th pin by resistance R1, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the first connecting resistance Rc11 of 6th pin is in parallel with electric capacity C11's, connecting resistance Rc12 and electric capacity C12's is in parallel again, connecting resistance Rc13 and electric capacity C13 again in parallel after connect the 7th pin, 7th pin connects the 13rd pin by resistance R13, the 2nd pin of U2 is connect by potentiometer R22, connect the 1st pin of U4, the 2nd pin of U5 is connect by resistance Ra1, connect the 5th pin of U7, connect the 2nd pin of U8, connect the 1st pin of U9, 8th pin connects the 9th pin by resistance R25, 13rd pin connects the 14th pin by resistance R14, 14th pin connects the 2nd pin by potentiometer R11,

1st pin of described operational amplifier U2 is connected with the 2nd pin by resistance Ry, connected with the 6th pin by resistance R2, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the first connecting resistance Rc21 of 6th pin is in parallel with electric capacity C21's, connect the in parallel of Rc22 and electric capacity C22 again, connect again Rc23 and electric capacity C23 in parallel after connect the 7th pin, 7th pin is connected with the 2nd pin by potentiometer R23, the 9th pin of U1 is connect by resistance R24, the 2nd pin of U1 is connect by potentiometer R12, the 13rd pin of U5 is connect by Ra6, connect the 11st pin of U7, connect the 13rd pin of U8, connect the 1st pin of U10, 8th pin connects the 13rd pin by resistance R33, first connect the in parallel of Rc31 and electric capacity C31, connect the in parallel of Rc32 and electric capacity C32 again, connecting resistance Rc33 and electric capacity C33 again in parallel after connect the 9th pin, 13rd pin connects the 14th pin by resistance R34, 14th pin connects the 2nd pin of U3 by potentiometer R32, connect the 3rd pin of U4,

Described operational amplifier U3 the 1st pin is connected with the 2nd pin by resistance Rz, connected by the 9th pin of resistance R3 and U2, U3 the 2nd pin connects 14 pins of U2 by R32,3rd pin ground connection, 4th pin meets VCC, 5th pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 10th pin, the 12nd pin, the 13rd pin, the 14th pin are unsettled, and the 11st pin meets VEE;

1st pin of described multiplier U4 connects the 7th pin of U1, and the 3rd pin connects the 14th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin completes overpotential device R21 connects the 2nd pin of U2, and the 8th pin meets VCC;

1st pin of described operational amplifier U5 connects the 2nd pin by diode D3, 2nd pin connects the 7th pin of U1 by resistance Ra1, by series connection the 1st pin of resistance Ra2 and diode D4, by series connection the 6th pin of resistance Ra1 and resistance Ra5, by series connection the 6th pin of resistance Ra2 and Ra3, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin connects positive 14V power supply, 11st pin connects negative 14V power supply, 6th pin connects the 7th pin by resistance Ra4, 7th pin connects the 7th pin of U6, 8th pin connects the 5th pin of U6, the 9th pin is connect by resistance Ra9, 9th pin is by series connection the 14th pin of resistance Ra8 and diode D6, by series connection the 13rd pin of resistance Ra10 and Ra6, 13rd pin is by series connection the 14th pin of resistance Ra7 and diode D6, 14th pin connects the 13rd pin by diode D5,

1st pin of described analog switch U6 connects the 2nd pin of U7, and the 2nd pin, the 14th pin connect positive 14V power supply, and the 3rd pin connects negative 14V power supply, 4th pin connects the 7th pin of U10, and the 5th pin connects the 8th pin of U5, and the 6th pin connects the 7th pin of U9,7th pin connects the 7th pin of U5, and the 8th pin connects the 2nd pin of U3 by potentiometer R31, the 9th pin, 10th pin, 11st pin, the 12nd pin, the 13rd pin is unsettled, 15th pin ground connection, the 16th pin connects the 13rd pin of U7;

1st pin of described voltage comparator U7, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 14th pin are unsettled, 3rd pin meets VCC, 4th pin, the 10th pin, the 12nd pin ground connection, 2nd pin connects positive 14V power supply by resistance R01, by the series connection ground connection of diode D1 and resistance R02,13rd pin connects positive 14V power supply by resistance R03, by the series connection ground connection of diode D2 and resistance R04;

1st pin of described operational amplifier U8 connects the 6th pin by resistance Rs1,2nd pin connects the 7th pin of U1,3rd pin, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin connects positive 14V power supply, and the 11st pin connects negative 14V power supply, 6th pin connects the 7th pin by resistance Rs2,7th pin connects the 3rd pin of U10, and the 8th pin connects the 3rd pin of U9, connects the 9th pin by Rs4,9th pin connects the 14th pin by resistance Rs3, and the 13rd pin connects the 7th pin of U2;

1st pin of described multiplier U9 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U8, the 2nd pin, the 4th pin, the 6th pin ground connection, and the 5th pin meets VEE, and the 7th pin connects the 6th pin of U6, and the 8th pin meets VCC;

1st pin of described multiplier U10 connects the 7th pin of U2, and the 3rd pin connects the 7th pin of U8, the 2nd pin, the 4th pin, the 6th pin ground connection, and the 5th pin meets VEE, and the 7th pin connects the 4th pin of U6, and the 8th pin meets VCC.

2. based on the fractional order four systems automatic switchover analog circuit of Lorenz type system, it is characterized in that being, by operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 and multiplier U4, multiplier U9, multiplier U10 and voltage comparator U7 and analog switch U6 forms, described operational amplifier U1 connects voltage comparator U7, operational amplifier U5, operational amplifier U8, multiplier U4, operational amplifier U2, described operational amplifier U2 concatenation operation amplifier U1, operational amplifier U5, voltage comparator U7, operational amplifier U8, described operational amplifier U3 concatenation operation amplifier U2, multiplier U4, described operational amplifier U5 connecting analog switch U6, described voltage comparator U7 connecting analog switch U6, described operational amplifier U8 concatenation operation amplifier U5, multiplier U9, multiplier U10, described multiplier U9 connecting analog switch U6, described multiplier U10 connecting analog switch U6,

1st pin of described operational amplifier U1 is connected with the 2nd pin by resistance Rx, connected with the 6th pin by resistance R1, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the first connecting resistance Rc11 of 6th pin is in parallel with electric capacity C11's, connecting resistance Rc12 and electric capacity C12's is in parallel again, connecting resistance Rc13 and electric capacity C13 again in parallel after connect the 7th pin, 7th pin connects the 13rd pin by resistance R13, the 2nd pin of U2 is connect by potentiometer R22, connect the 1st pin of U4, the 2nd pin of U5 is connect by resistance Ra1, connect the 5th pin of U7, connect the 2nd pin of U8, connect the 1st pin of U9, 8th pin connects the 9th pin by resistance R25, 13rd pin connects the 14th pin by resistance R14, 14th pin connects the 2nd pin by potentiometer R11,

1st pin of described operational amplifier U2 is connected with the 2nd pin by resistance Ry, connected with the 6th pin by resistance R2, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the first connecting resistance Rc21 of 6th pin is in parallel with electric capacity C21's, connect the in parallel of Rc22 and electric capacity C22 again, connect again Rc23 and electric capacity C23 in parallel after connect the 7th pin, 7th pin is connected with the 2nd pin by potentiometer R23, the 9th pin of U1 is connect by resistance R24, the 2nd pin of U1 is connect by potentiometer R12, the 13rd pin of U5 is connect by Ra6, connect the 11st pin of U7, connect the 13rd pin of U8, connect the 1st pin of U10, 8th pin connects the 13rd pin by resistance R33, first connect the in parallel of Rc31 and electric capacity C31, connect the in parallel of Rc32 and electric capacity C32 again, connecting resistance Rc33 and electric capacity C33 again in parallel after connect the 9th pin, 13rd pin connects the 14th pin by resistance R34, 14th pin connects the 2nd pin of U3 by potentiometer R32, connect the 3rd pin of U4,

Described operational amplifier U3 the 1st pin is connected with the 2nd pin by resistance Rz, connected by the 9th pin of resistance R3 and U2, U3 the 2nd pin connects 14 pins of U2 by R32,3rd pin ground connection, 4th pin meets VCC, 5th pin, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 10th pin, the 12nd pin, the 13rd pin, the 14th pin are unsettled, and the 11st pin meets VEE;

1st pin of described multiplier U4 connects the 7th pin of U1, and the 3rd pin connects the 14th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin completes overpotential device R21 connects the 2nd pin of U2, and the 8th pin meets VCC;

1st pin of described operational amplifier U5 connects the 2nd pin by diode D3, 2nd pin connects the 7th pin of U1 by resistance Ra1, by series connection the 1st pin of resistance Ra2 and diode D4, by series connection the 6th pin of resistance Ra1 and resistance Ra5, the 6th pin is connect after series connection by resistance Ra2 and Ra3, 3rd pin, 5th pin, 10th pin, 12nd pin ground connection, 4th pin connects positive 14V power supply, 11st pin connects negative 14V power supply, 6th pin connects the 7th pin by resistance Ra4, 7th pin connects the 7th pin of U6, 8th pin connects the 5th pin of U6, the 9th pin is connect by resistance Ra9, 9th pin is by series connection the 14th pin of resistance Ra8 and diode D6, by series connection the 13rd pin of resistance Ra10 and Ra6, 13rd pin is by series connection the 14th pin of resistance Ra7 and diode D6, 14th pin connects the 13rd pin by diode D5,

1st pin of described analog switch U6 connects the 2nd pin of U7, and the 2nd pin, the 14th pin connect positive 14V power supply, and the 3rd pin connects negative 14V power supply, 4th pin connects the 7th pin of U10, and the 5th pin connects the 8th pin of U5, and the 6th pin connects the 7th pin of U9,7th pin connects the 7th pin of U5, and the 8th pin connects the 2nd pin of U3 by potentiometer R31, the 9th pin, 10th pin, 11st pin, the 12nd pin, the 13rd pin is unsettled, 15th pin ground connection, the 16th pin connects the 13rd pin of U7;

1st pin of described voltage comparator U7, the 6th pin, the 7th pin, the 8th pin, the 9th pin, the 14th pin are unsettled, 3rd pin meets VCC, 4th pin, the 10th pin, the 12nd pin ground connection, 2nd pin connects positive 14V power supply by resistance R01, by the series connection ground connection of diode D1 and resistance R02,13rd pin connects positive 14V power supply by resistance R03, by the series connection ground connection of diode D2 and resistance R04;

1st pin of described operational amplifier U8 connects the 6th pin by resistance Rs1,2nd pin connects the 7th pin of U1,3rd pin, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin connects positive 14V power supply, and the 11st pin connects negative 14V power supply, 6th pin connects the 7th pin by resistance Rs2,7th pin connects the 3rd pin of U10, and the 8th pin connects the 3rd pin of U9, connects the 9th pin by Rs4,9th pin connects the 14th pin by resistance Rs3, and the 13rd pin connects the 7th pin of U2;

1st pin of described multiplier U9 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U8, the 2nd pin, the 4th pin, the 6th pin ground connection, and the 5th pin meets VEE, and the 7th pin connects the 6th pin of U6, and the 8th pin meets VCC;

1st pin of described multiplier U10 connects the 7th pin of U2, and the 3rd pin connects the 7th pin of U8, the 2nd pin, the 4th pin, the 6th pin ground connection, and the 5th pin meets VEE, and the 7th pin connects the 4th pin of U6, and the 8th pin meets VCC.