WO2013071689A1

WO2013071689A1 - Method and analog circuit for implementing automatic switching of chaotic systems of integer order and fractional order

Info

Publication number: WO2013071689A1
Application number: PCT/CN2012/001384
Authority: WO
Inventors: 王忠林
Original assignee: Wang Zhonglin
Priority date: 2011-11-18
Filing date: 2012-10-15
Publication date: 2013-05-23
Also published as: CN102497263A; CN102497263B

Abstract

The structure of an automatic switching chaotic system of an integer order and a fractional order, and an analog circuit implementation method are disclosed. The method comprises: an integer order chaotic system and a fractional order chaotic system forming an automatic switching system, and implementing the automatic switching chaotic system by using the analog circuit. Through the present invention, automatic switching between the integer order chaotic system and the fractional order chaotic system is implemented by using the analog circuit. The automatic switching chaotic system of the integer order and the fractional order is more complicated than the integer order chaotic system, the fractional order chaotic system, and the automatic switching system, and has the advantages of the three. The system provided by the present invention makes great sense in chaos-based secure communications and signal detection, and has desirable application prospects.

Description

Method and analog circuit for realizing integer-order and fractional-order automatic switching chaotic system

The invention relates to a method for realizing an integer-order and fractional-order automatic switching chaotic system by using an analog circuit, in particular to a method and an analog circuit for realizing an integer-order and fractional-order automatic switching chaotic system.

Background technique

Methods for implementing integer-order chaotic systems with analog circuits There are many reports in the literature. Methods for implementing fractional-order chaotic systems with analog circuits are also reported in the literature. Methods and circuit literature for implementing automatic switching chaotic systems have also been reported, but with analog circuits. The method and circuit for implementing automatic switching chaotic systems with integer order and fractional order have not been reported, because chaotic systems with integer order and fractional order automatic switching are more complex than integer order chaotic systems, fractional chaotic systems and automatic switching systems. Therefore, a design method of integer-order and fractional-order automatic switching chaotic systems is proposed, and the chaotic system is realized by analog circuits, which is of great significance for the application of such chaotic systems.

Summary of the invention

The technical problem to be solved by the present invention is to provide a method and an analog circuit for an integer-order and fractional-order automatic switching chaotic system.

The invention adopts the following technical means to achieve the object of the invention:

A method for realizing an integer order and fractional order automatic switching chaotic system, characterized in that the method comprises the following steps: (1) According to the integer order chaotic system i:

Dx l dt - a(y - x)

Dx / dt = bx + cy - xz

Dxl dt - x' - hz

i a=20, b=14, c=10.6, h=2.8

(2) According to the fractional order chaotic system ii is:

d ^q XI dt ^q = a(y - x)

d ^q y I df = bx + cy-xz

d"zl dt ^q = x ² - hz

Ii 0<q<l, a=20, b=14, c=10.6, h=2.8

(3) Constructing a selection function system iii to form chaotic systems i and ii into a new integer-order and fractional-order automatic switching mixture v _:

(4) Construct the analog circuit system according to chaotic systems iii and iv, and obtain the analog high and low level by using voltage comparator U6, x>=0 and x<0, as the input of the selection function, realize the integer order by using analog switches U7 and U8. The alternating output of integral and fractional integration, using the operational amplifiers Ul, U2, U3 and multipliers U4, U5 to obtain the analog circuit of the integer order and fractional automatic switching chaotic system. The operational amplifiers Ul, U2, U3 adopt LF347, the multipliers U4, U5 adopt AD633JN, the voltage comparator U6 adopts LM339, the analog switches U7, U8 adopt CD4052;

The operational amplifier U1 is connected to a voltage comparator U6, analog switches U7, U8, multipliers U4, U5, the voltage comparator U6 is connected to analog switches U7, U8, and the multiplier U4 is connected to an operational amplifier U2, the operational amplifier U2 is connected to the analog switch U7, the multiplier U5 is connected to the operational amplifier U3, and the operational amplifier U3 is connected to the analog switch U8;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and is connected to the sixth pin of U1 through the resistor R1, and the third, fifth, ten, and 12th pins are grounded, and the fourth pin is connected. Connect to VCC, the 11th pin is connected to VEE, the 6th pin is connected in parallel with the resistor Rcl l and the capacitor C 1 1 , then connected in parallel with Rcl2 and capacitor C 12, and then connected in parallel with Rcl 3 and capacitor C13, The 4th pin of U7 is connected, the capacitor C 10 is connected to the 5th pin of U7, the 7th pin is connected to the 9th pin of U6, and the 1st pin of U4 is connected, and the U7 is connected. The 9-pin is connected to the first and third pins of U5, and the second pin of U2 is connected through the resistor R22. The eighth pin I is connected to the 9th pin of U1 through the resistor R25. The pin is connected to the second pin of U1 through the resistor R24 and the potentiometer R12, and is connected to the second pin of U2 through the resistor R24 and the potentiometer R23, and is connected to the 10th pin of the U7 through the resistor R24, and the 13th pin is passed. The resistor R13 is connected to the 7th pin of U1, is connected to the 14th pin of U1 through the resistor R14, is connected to the 1st pin of U4, is connected to the 8th pin of U7, and is connected to the 1st pin of U5. The third pin is connected, and the 14th pin is passed through the potentiometers R11 and U. 1 The second pin is connected; the first pin of the operational amplifier U2 is connected to the first pin through the resistor Ry, and is connected to the sixth pin of the U2 through the resistor R2, the third, fifth, ten, and twelve The pin is grounded, the fourth pin is connected to VCC, the eleventh pin is connected to VEE, the sixth pin is connected in parallel with the resistor Rc21 and the capacitor C21, and then connected in parallel with Rc22 and capacitor C22, and connected to R _c 23 and capacitor C23. After parallel connection, it is connected to the 13th pin of U7, through the capacitor C20 and the 12th pin of U7, the 7th pin is connected with the 9th pin of U7, the 8th pin and the 8th pin of U8 The pin is connected, the 9th pin is connected in parallel with the resistor Rc33 and the capacitor C33, and then connected in parallel with the Rc32 and the capacitor C32, and then connected in parallel with the capacitor C31, and connected to the 4th pin of the U8, through the capacitor C30. It is connected to the 5th pin of U8. The 13th pin is connected to the 3rd pin of U4 through the resistor R33, and is connected to the 8th pin of U8 through the resistor R33, and is connected to the 14th pin of U2 through the resistor R34. 14th bow | foot connected U4 The third pin is connected to the second pin of U3 through the potentiometer R32;

The first pin of the operational amplifier U3 is connected to the first pin through the resistor Rz, and is connected to the ninth pin of the U2 through the resistor R31, and the second pin of the U3 is connected to the 14 pin of the U2 through the R32, the third pin. Grounding, the 4th pin is connected to VCC, the 5th, 6th, 7th, 8th, 9th, 10th, 12th, 13th, 14th are all suspended, the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the third pin of U1, the third pin is connected to the 14th pin of U2, the second, fourth, and sixth pins are grounded, and the fifth pin is connected to VEE, 7 pin is connected to the second pin of U2 through resistor R21, and the eighth pin is connected to VCC;

The first and third pins of the multiplier U5 are connected to the seventh pin of U1, the second, fourth, and sixth pins are grounded, the fifth pin is connected to VEE, and the seventh pin is connected to the U3 through the resistor R31. 2 pins, the 8th pin is connected to VCC;

The first, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13 pins of the voltage comparator U6 are left floating, the third pin is connected to VCC; the eighth pin is passed through the resistors R02 and U7. The first pin and the first pin of U8 are connected, the 12th pin is connected to VEE, and the 14th pin is connected to the first pin of U7 and the first pin of U8 through diode D1, and is connected through the resistor R01. VCC;

The first pin of the analog switch U7 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 6 pin of U1 through the fractional integration unit. The 5th pin is connected to the 6 pin of U1 through the capacitor C10, the 8th pin is connected to the 7 pin of U1, the 9th pin is connected to the 7 pin of U2, and the 12th pin is connected to the 6 pin of U2 through C20. The 13th pin is connected to the 6 pin of U2 through the fractional integration unit, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded.

The first pin of the analog switch U8 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 9 pin of U2 through the fractional integration unit. The 5th pin is connected to the 9 pin of U2 through the capacitor C30, the 8th pin is connected to the 8 pin of U2, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded.

2. A circuit for implementing an integer-order and fractional-order β-switching chaotic system, comprising: an operational amplifier U1, U2, U3 and a multiplier U4, U5 and a voltage comparator U6 and an analog switch U7, U8, The operational amplifier U1 is connected to a voltage comparator U6, analog switches U7, U8, multipliers U4, U5, the voltage comparator U6 is connected to analog switches U7, U8, and the multiplier U4 is connected to an operational amplifier U2, the operational amplifier U2 is connected to the analog switch U7, the multiplier U5 is connected to the operational amplifier U3, the operational amplifier U3 is connected to the analog switch U8;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and is connected to the sixth pin of U1 through the resistor R1, and the third, fifth, ten, and 12th pins are grounded, and the fourth pin is connected. Connect to VCC, the 11th bow|female is connected to VEE, the 6th pin is connected in parallel with the resistor Rcll and the capacitor C11, then the parallel connection of Rcl2 and capacitor C12, and the parallel connection of Rcl3 and capacitor C13, and the fourth lead of U7 The pins are connected, through the capacitor C10 and the fifth pin of U7, the seventh pin and the U6 The 9th pin is connected, connected to the 1st pin of U4, connected to the 9th pin of U7, connected to the 1st and 3rd pins of U5, and connected to the 2nd pin of U2 through the resistor R22. The 8th pin is connected to the 9th pin of U1 through the resistor R25, and the 9th pin is connected to the 2nd pin of U1 through the resistor R24 and the potentiometer R12, through the resistor R24 and the potentiometer R23 and the U2 pin 2 Connected, through the resistor R24 and U7 10th pin, the 13th pin is connected to the 7th pin of U1 through the resistor R13, through the resistor R14 and the 14th pin of U1, and the 1st pin of U4 Connected to the 8th pin of U7, connected to the 1st and 3rd pins of U5, the 14th pin is connected to the 2nd pin of U1 through potentiometer R1 1; The first pin of U2 is connected to the second pin through the resistor Ry, the sixth pin of U2 is connected through the resistor R2, the third, fifth, ten, and 12 pins are grounded, and the fourth pin is connected to VCC. 11 pin is connected to VEE, the 6th pin is connected in parallel with the capacitor R21 and the capacitor C21. Then, the parallel connection between Rc22 and the capacitor C22 is connected, and the parallel connection between the Rc23 and the capacitor C23 is connected to the 13th pin of the U7. Through the capacitor C20 and the 12th pin of U7 The 7th pin is connected to the 9th pin of U7, the 8th pin is connected to the 8th pin of U8, the 9th pin is connected in parallel with the resistor Rc33 and the capacitor C33, and then the parallel connection of Rc32 and capacitor C32 is connected. After connecting Rc31 and capacitor C31 in parallel, it is connected to the 4th pin of U8, and is connected to the 5th pin of U8 through capacitor C30. The 13th pin is connected to the 3rd pin of U4 through resistor R33. Connected to the 8th pin of U8 through resistor R33, connected to pin 14 of U2 through resistor R34, pin 14 is connected to pin 3 of U4, and connected to pin 2 of U3 via potentiometer R32:

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, and is connected to the ninth pin of the U2 through the resistor R31, and the second pin of the U3 is connected to the 14 pin of the U2 through the R32. The ground is grounded, the 4th pin is connected to VCC, the 5th, 6th, 7th, 8th, 9th, 10th, 12th, 13th and 14th are all 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 14th pin of U2, the second, fourth, and sixth pins are grounded, and the fifth pin is connected to VEE, the seventh pin. The pin is connected to the second pin of U2 through the resistor R21, and the eighth pin is connected to VCC;

The first, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13 pins of the voltage comparator U6 are left floating, the third pin is connected to VCC; the eighth pin is passed through the resistors R02 and U7. The first pin I and the first pin of U8 are connected, the 12th pin is connected to VEE, and the 14th pin is connected to the first pin of U7 and the first pin of U8 through diode D1. R01 is connected to VCC;

The first pin of the analog switch U7 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 6 pin of U1 through the fractional integration unit. The 5th pin is connected to the 6 pin of U1 through the capacitor C10, the 8th pin is connected to the 7 pin of U1, the 9th pin is connected to the 7 pin of U2, and the 12th pin is connected to the U2 through C20. The 6 pin, the 13th pin is connected to the 6 pin of U2 through the fractional integration unit, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded;

DRAWINGS

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

Figure 2 shows the structure of the peripheral circuit of the operational amplifier U1.

Figure 3 shows the structure of the peripheral circuits of the operational amplifier U2 and the multiplier U4.

Figure 4 shows the structure of the peripheral circuits of the operational amplifier U3 and the multiplier U5.

Figure 5 is a schematic diagram showing the structure of the peripheral circuit of the voltage comparator U6.

Figure 6 is a schematic diagram showing the structure of the peripheral circuit of the analog switch U7.

Figure 7 is a schematic diagram showing the structure of the peripheral circuit of the analog switch U8.

detailed description

The invention will now be described in further detail with reference to the drawings and preferred embodiments.

Referring to Figures 1-7, an integer-order and fractional-order automatic switching chaotic system is first constructed. An integer-order chaotic system i selected in the preferred embodiment is:

Dxl dt = a{y-x)

Dxl dt-bx + cy-xz

Dxl dt = x ² -h∑

a=20, b=14, c=10.6, h=2.8

The selected fractional chaotic system ii is:

d"x/dt ⁹ ^a(yx)

d ^q y I df =bx + cy-xz

d ^q zl d =x ² -hz

Ii 0<q<l, a=20, b=14, c=10.6, h=2.8

Construct a selection function system iii, and combine chaotic systems i and ii into a new integer-order and fractional-order automatic switching chaotic system iv:

d ^f{x) x / dt ^f(x) = a(y - x)

' d ^f{x) y I dt ^{f )} ^ bx + cy - xz

d ^f[x) z / dt ^{f )} ^ x ² - hz

Iv

According to system iii and integer-order and fractional-order automatic switching chaotic system iv to construct an analog circuit, using voltage comparator U6 to obtain the analog high and low level, x>=0 and x<0, as the input of the selection function, using analog switch U7 and U8 realizes the alternating output of integer order integral and fractional integral, and uses the operational amplifiers Ul, U2, U3 and multipliers U4, U5 to obtain the analog circuit of the integer order and fractional automatic switching chaotic system. The operational amplifiers U1, U2, U3 are LF347, the multipliers U4, U5 are AD633JN, the voltage comparator U6 is LM339, the analog switches U7, U8 are CD4052; the operational amplifier U1 is connected to the voltage comparator U6, the analog switch U7 U8, multiplier U4, U5, the voltage comparator U6 is connected to the analog switches U7, U8, the multiplier U4 is connected to the operational amplifier U2, the operational amplifier U2 is connected to the analog switch U7, and the multiplier U5 is connected to the operational amplifier U3, the operational amplifier U3 is connected to the analog switch U8;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and is connected to the sixth pin of U1 through the resistor R1, and the third, fifth, ten, and 12th pins are grounded, and the fourth pin is connected. Connect to VCC, the 11th pin is connected to VEE, the 6th pin is connected in parallel with the resistor Rcl l and the capacitor C11, then the parallel connection of Rcl2 and capacitor C12, and the parallel connection of Rcl3 and capacitor C13, and the fourth lead of U7 The pin is connected, the capacitor C10 is connected to the fifth pin of U7, the seventh pin is connected to the 9th pin of U6, and is connected to the first pin of U4, and is connected to the 9th pin of U7. It is connected to the first and third pins of U5, and is connected to the second pin of U2 through the resistor R22. The eighth pin is connected to the 9th pin of U1 through the resistor R25, and the 9th pin is connected to the potential R24 and the potential. R12 is connected to the second pin of U1, and is connected to the second pin of U2 through the resistor R24 and the potentiometer R23, and is connected to the 10th pin of U7 through the resistor R24, and the 13th pin is passed through the resistor R13 and U1. The pin is connected, connected to the 14th pin of U1 through the resistor R14, connected to the 1st pin of U4, connected to the 8th pin of U7, and the 1st pin and the 3rd pin of U5. Connect, the 14th pin through the potentiometer R11 and U1 2nd lead The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, and is connected to the sixth pin of U2 through the resistor R2, and the third, fifth, ten, and 12th pins are grounded. The fourth pin is connected to VCC, the eleventh pin is connected to VEE, the sixth pin is connected in parallel with the resistor Rc21 and the capacitor C21, and then connected in parallel with Rc22 and capacitor C22, and then connected in parallel with Rc23 and capacitor C23, and U7. The 13th pin is connected, the capacitor C20 is connected to the 12th pin of U7, the 7th pin is connected to the 9th pin of U7, and the 8th pin is connected to the 8th pin of U8, the 9th pin The pin is connected in parallel with the capacitor R33 and the capacitor C33, and then connected in parallel with the capacitor C32, and then connected in parallel with the capacitor C31, and connected to the fourth pin of the U8, through the fifth lead of the capacitor C30 and U8. The pin is connected, the 13th pin is connected to the 3rd pin of U4 through the resistor R33, the 8th pin of the U8 is connected through the resistor R33, the 14th pin of the U2 is connected through the resistor R34, and the 14th pin is connected to the U4. The third pin is connected to the second pin of U3 through the potentiometer R32;

The first and third pins of the multiplier U5 are connected to the third pin of U1, the second, fourth, and sixth pins are grounded, the fifth pin is connected to VEE, and the seventh pin is connected to the U3 through the resistor R31. 2 pins, the 8th pin is connected to VCC;

The first, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13 pins of the voltage comparator U6 are left floating, the third pin is connected to VCC; the eighth pin is passed through the resistors R02 and U7. The first pin and the first pin of U8 are connected, the 12th pin is connected to VEE, and the 14th pin is connected to the first pin of W and the first pin of U8 through diode D1, and is connected through the resistor R01. VCC;

The first pin of the analog switch U7 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 6 pin of U1 through the fractional integration unit. The 5th pin is connected to the 6 pin of U1 through the capacitor C10, the 8th pin is connected to the 1 pin of U1, the 9th pin is connected to the Ί pin of U2, and the 12th pin is connected to the 6 pin of U2 through C20. The 13th pin is connected to the 6 pin of U2 through the fractional integration unit, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded.

The above description is not intended to limit the invention, and the invention is not limited to the above examples, and variations, modifications, additions or substitutions made by those skilled in the art within the scope of the invention also belong to the invention. protected range.

Claims

Claim

A method for realizing an integer order and fractional order automatic switching chaotic system, characterized in that the method comprises the following steps:

(1) According to the integer order chaotic system i is:

Dxl dt = a(y-x)

Dx/ dt = bx + cy-xz i a=20, b=14, c=10.6, h=2.8

Dxl dt- x ¹ ~ hz

(2) According to the fractional order chaotic system ii is:

d ^q xl df = a(yx)

- d ^q yldt ^q ^bx + cy-xz ii 0<q<l, a=20, b=14,c=10.6,h=2.8

d ^q z I df =x ² -hz

(3) Construct a selection function system iii to form chaotic systems i and ii into a new integer-order and fractional-order automatic switching chaotic system iv:

'd ^fix) x/dt ^f(x) = a(yx)

Xz iv

(4) According to the chaotic system iii and iv, the analog circuit system is constructed, and the analog high and low level is obtained by the voltage comparator U6, x>=0 and x<0, as the input of the selection function, and the integer order is realized by the analog switches U7 and U8. The alternating output of integral and fractional integration uses the operational amplifiers Ul, U2, U3 and multipliers U4, U5 to obtain an analog circuit that automatically switches chaotic systems with integer order and fractional. The operational amplifiers Ul, U2, U3 use LF347, the multipliers U4, U5 use AD633JN, the voltage comparator U6 uses LM339, the analog switches U7, U8 use CD4052;

The operational amplifier U1 is connected to a voltage comparator U6, analog switches U7, U8, multipliers U4, U5, the voltage comparator U6 is connected to analog switches U7, U8, and the multiplier U4 is connected to an operational amplifier U2, the operational amplifier U2 is connected to the analog switch U7, the multiplier U5 is connected to the operational amplifier U3, the operational amplifier U3 is connected to the analog switch U8;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and passes through the resistor R1. Connected to the 6th pin of Ul, the third,

5, 10, 12 pins are grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is connected in parallel with the resistor Rcl l and the capacitor C11, and then Rcl 2 is connected in parallel with the capacitor C12. Connect Rc l 3 and capacitor C13 in parallel, connect with the 4th pin of U7, connect the 5th pin of U7 through capacitor C10, the 7th pin and the 9th pin of U6, and U4 The first pin is connected, connected to the 9th pin of U7, connected to the 1st and 3rd pins of U5, connected to the 1st pin of U2 through the resistor R22, and the 8th pin is connected to the U1 through the resistors R25 and U1. The 9th pin is connected, the 9th pin is connected to the 2nd pin of U1 through the resistor R24 and the potentiometer R12, and the 2nd pin of the potentiometer R23 and 112 is connected through the resistor R24, and the 10th through the resistor R24 and U7 The pin is connected, the 13th pin is connected to the 7th pin of U1 through the resistor R13, the 14th pin of U1 is connected through the resistor R14, the 1st pin of U4 is connected, and the 8th pin of U7 Connected to the first pin and the third pin of U5, the 14th pin is connected to the second pin of U1 through the potentiometer R11;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, and is connected to the sixth pin of the U2 through the resistor R2, and the third, fifth, ten, and 12th pins are grounded, and the fourth pin is connected. Connect to VCC, the 11th pin is connected to VEE, the 6th pin is connected in parallel with the resistor Rc21 and the capacitor C21, then the parallel connection of Rc22 and capacitor C22, and the parallel connection of Rc23 and capacitor C23, and the 7th lead of U7 The pin is connected, through the capacitor C20 and the 12th pin of U7, the 7th pin is connected with the 9th pin of U7, the 8th pin is connected with the 8th pin of U8, the 9th pin is first Connect the resistor Rc33 and the capacitor C33 in parallel, and then connect Rc 32 and capacitor C32 in parallel, connect Rc 31 and capacitor C31 in parallel, connect with U8 pin 4, pass capacitor C30 and U8 pin 5. Connected, the 1st 3 pin is connected to the 3rd pin of U4 through the resistor R33, the 8th pin of U8 is connected through the resistor R33, the 14th pin of U2 is connected through the resistor R34, and the 14th pin is connected to the U4. The third pin is connected to the second pin of U3 through the potentiometer R32;

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, and is connected to the ninth pin of the U2 through the resistor R31, and the second pin of the U3 is connected to the 14 pin of the U ² through the R32, the third pin. Pin ground, the fourth pin is connected to VCC, the fifth,

6,

7,

8,

9,

1 0, 12, 1 3, 14 are all suspended, the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the seventh pin of U1, and the third pin is connected to the 14th pin of U2. Pins, pins 2, 4, and 6 are grounded, the fifth pin is connected to VEE, the seventh pin is connected to the second pin of U2 through the resistor R21, and the eighth pin is connected to VCC;

1, 2, 4, 5, 6, 7, 9, 10 of the voltage comparator U6,

11,

12, 13 pins are left floating, the third pin is connected to VCC; the 8th pin is connected to the 1st pin of U7 and the 1st pin of U8 through the resistor R02, the 12th pin is connected to VEE, the 14th pin is passed Diode D1 is connected to the first pin of U7 and the first pin of U8, and is connected to VCC through resistor R01;

The first pin of the analog switch U7 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 6 pin of U1 through the fractional integration unit. The 5th pin is connected to the 6 pin of U1 through the capacitor C10, the 8th pin is connected to the 7 pin of U1, the 9th pin is connected to the 7 pin of U2, and the 12th pin is connected to the 6 pin of U2 through C20. The 13th pin is connected to the 6 pin of U2 through the fractional integration unit, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded;

2. A circuit for realizing an integer-order and fractional-order automatic switching chaotic system, comprising: an operational amplifier U1, U2, U3 and a multiplier U4, U5 and a voltage comparator U6 and an analog switch U7, U8, The operational amplifier U1 is connected to the voltage comparator U6, the analog switches U7, U8, the multipliers U4, U5, the voltage comparator U6 is connected to the analog switches U7, U8, and the multiplier U4 is connected to the operational amplifier U2, the operational amplifier U2 Connecting the analog switch U7, the multiplier U5 is connected to the operational amplifier U3, the operational amplifier U3 is connected to the analog switch U8;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and is connected to the sixth pin of U1 through the resistor R1, and the third, fifth, ten, and 12th pins are grounded, and the fourth pin is connected. Connected to VCC, 11th The pin is connected to VEE. The 6th pin is connected in parallel with the capacitor R11 and the capacitor C11. Then, the Rcl 2 is connected in parallel with the capacitor C12. After the Rcl 3 is connected in parallel with the capacitor C1 3, it is connected to the 4th pin of the U7. The capacitor C10 is connected to the fifth pin of U7, the seventh pin is connected to the ninth pin of U6, and is connected to the first pin of U4, and is connected to the ninth pin of U7, and U5. The first and third pins are connected, and the second pin of U2 is connected through the resistor R22. The eighth pin is connected to the 9th pin of U1 through the resistor R25, and the 9th pin is connected to the R24 and the potentiometer R12 through the resistor R22. U1 pin 2 is connected, through resistor R24 and potentiometer R23 and U2 pin 2, through resistor R24 and U7 pin 10, pin 13 through resistor R13 and U1 pin 7 Connected to the 14th pin of U1 through resistor R14, connected to the 1st pin of U4, connected to the 8th pin of U7, and connected to the 1st and 3rd pins of U5. The 14th pin is connected to the 2nd pin of U1 through the potentiometer R11;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, and is connected to the sixth pin of U2 through the resistor R2, and the third, fifth, ten, and 12 pins are grounded, and the fourth lead The pin is connected to VCC, the 11th pin is connected to VEE, the 6th pin is connected in parallel with the resistor Rc21 and the capacitor C21. Then, the parallel connection between Rc22 and capacitor C22 is connected, and the parallel connection between Rc23 and capacitor C23 is made. The pin is connected, the capacitor C20 is connected to the 12th pin of U7, the 7th pin is connected to the 9th pin of U7, the 8th pin is connected to the 8th pin of U8, the 9th pin First connect the resistor Rc 33 and the capacitor C33 in parallel, then connect Rc 32 and capacitor C32 in parallel, connect Rc 31 and capacitor C31 in parallel, connect with U8 pin 4, pass capacitor C30 and U8 5 The pin is connected, the 13th pin is connected to the 3rd pin of U4 through the resistor R33, the 8th pin of U8 is connected through the resistor R33, and the 14th pin of U2 is connected through the resistor R34, the 14th pin Connect the third pin of U4 to the second pin of U3 through potentiometer R32;

The first pin of the operational amplifier U3 is connected to the second pin through the resistor Rz, and is connected to the ninth pin of the U2 through the resistor R31, and the second pin of the U3 is connected to the 14 pin of the U2 through the R32, the third lead The ground is grounded, the 4th pin is connected to VCC, the 5th, 6th, 7th, 8th, 9th, 10th, 12th,

1 3, 14 are all suspended, the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the third pin of U1, the third pin is connected to the 14th pin of U2, the second, fourth, and sixth pins are grounded, and the fifth pin is connected to VEE, the seventh pin. Pin is connected to U ² through resistor R21 The second pin, the eighth pin is connected to VCC;

The first and third pins of the multiplier U5 are connected to the first pin of U1, the second, fourth, and sixth pins are grounded, the fifth pin is connected to VEE, and the seventh pin is connected to the U3 through the resistor R31. 2 pins, the 8th pin is connected to VCC;

The 1st, 1st, 4th, 5th, 6th, 7th, 9th, 10th, 11th, 12th, and 13th pins of the voltage comparator U6 are left floating, the third pin is connected to VCC; the eighth pin is passed through the resistors R02 and U7. The first pin and the first pin of U8 are connected, the 12th pin is connected to VEE, and the 14th pin is connected to the first pin of U7 and the first pin of U8 through diode D1, and is connected via resistor R01. VCC;

The first pin of the analog switch U7 is connected to the eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 6 pin of U1 through the fractional integration unit. The 5th pin is connected to the 6 pin of U1 through the capacitor C1 0, the 8 pin is connected to the 7 pin of U1, the 9th pin is connected to the 7 pin of U ² , and the 12th pin is connected to the 6 pin of U2 through C20. The 13th pin of the pin is connected to the 6 pin of U2 through the fractional integration unit, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded.

The first pin of the analog switch U8 is connected to the ^eighth pin of U6 through the resistor R02, the second pin is connected to VCC, the third pin is connected to VEE, and the fourth pin is connected to the 9 pin of U2 through the fractional integration unit. The 5th pin is connected to the 9 pin of U2 through the capacitor C30, the 8th pin is connected to the 8 pin of U2, the 14th pin is connected to VCC, and the 15th and 16th pins are grounded.