WO2014048052A1

WO2014048052A1 - Analog circuit and method for fractional-order four-system automatic switching chaotic system based on lü type system

Info

Publication number: WO2014048052A1
Application number: PCT/CN2013/000422
Authority: WO
Inventors: 王忠林
Original assignee: Wang Zhonglin
Priority date: 2012-09-27
Filing date: 2013-04-12
Publication date: 2014-04-03
Also published as: CN102904708B; CN102904708A

Abstract

Disclosed are an analog circuit and method for a fractional-order four-system automatic switching chaotic system based on a Lü type system, a method for realizing the analog circuit and the structure of the Lü type fractional-order four-system automatic switching chaotic system. The analog circuit consists of an operational amplifier U1, an operational amplifier U2, an operational amplifier U3, an operational amplifier U5, an operational amplifier U8, a multiplier U4, a multiplier U9, a multiplier U10, a voltage comparator U7 and an analog switch U6. The present invention utilizes an analog circuit to realize a fractional-order chaotic system having four Lü type sub-systems capable of automatically switching, is more complex and more random than an un-switching fractional-order chaotic system and an automatic switching chaotic system consisting of two or three chaotic sub-systems, and therefore can be a new choice as a signal source in secure communication, and have a better application prospect in secure communication.

Description

Method and analog circuit for automatically switching chaotic system based on fractional order four systems of Ltl type system

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

Background technique

At present, there are many ways to implement integer-order and fractional-order chaotic systems and circuits with analog circuits. However, there are few methods for implementing automatic switching chaotic circuits with analog circuits, and the disclosed automatic switching chaotic systems and circuits are integer orders. The method for chaotic system switching, the method and the circuit for automatically switching multiple sub-chaotic systems are not disclosed. The present invention provides a method and an analog circuit for automatically switching chaotic systems of LU-type fractional four systems, enriching the automatic switching chaotic system. The number and type of chaos increases the randomness of chaotic systems and has a good application prospect in secure communication.

Summary 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 based on fractional order of a type system.

The invention adopts the following technical means to achieve the purpose of the invention -

1. A method for automatically switching a chaotic system based on a fractional order of four systems of a LU type system, characterized in that it comprises the following steps

(1) According to the Lil chaotic system I is:

Dxl dt = a(y - x)

' dy l dt = -xz + cy

Dz l dt = \y [ - bz

(3) Chaotic system construction symbol functions III and IV are:

1

Replacement page (Article 26) (4) According to the Ltl type chaotic system V:

Dx I dt = a^y - x)

Dy/dt = -xz + cy V a=36, b=3, c=20

Dzl dt- xsign(y) - bz

(5) According to the LU type chaotic system VI:

Dx / dt = a(y - x)

Dyl dt = -xz + cy VI a=36, b=3, c=20

Dzl dt = ysign{x) - bz

(6) According to the chaotic system structure selection function VII is

(7) According to the system I, II, V, VI and the selection function VII, construct an Ltl-type four system to automatically switch the chaotic system IX dx/dt = (y~x)

Dy I dt = -xz + cy IX a=36, b=3, c=20

Dzl dt = f xy) - bz

(8) Construct a LU-type fractional four systems according to system IX to automatically switch chaotic systems X d ^q xl dt ^q = a{yx)

d ^q yl d =~xz + cy X 0<q<l, a=36, b=3,c=20

D'zldt" =f{xy)-bz

(9) According to the chaotic system X, the analog circuit system is constructed, and the voltage comparator U7 is used to obtain two simulated 髙 low levels, x>=0 or x<0 and y>=0 or y<0, as the analog switch U6. Control input, according to x>=0, y>=0, x>0 y<0, x<0, y>=0 and x<0, y<0, the difference of f(xy) is realized. The output is realized to realize the chaotic system IX of four systems automatic switching, and then the chaotic system X is realized by fractional integration, the operational amplifier U1, the operational amplifier U2, the operational amplifier U3, the operational amplifier U5, the operational amplifier U8 adopts LF347, the multiplier U4, Multiplier U9, multiplier U10 uses AD633J, analog switch U6 uses ADG409, voltage comparator U7 uses LM139;

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 through the resistor R1, and the third bow, the fifth bow, the tenth pin, and the third pin. 12-pin grounding, the fourth pin is connected to VCC, the eleventh pin is connected to VEE, the sixth pin is connected in parallel with the resistor Rcll and the capacitor C11, and then connected in parallel with the resistor Rcl2 and the capacitor C12, and connected to the resistor Rc and the capacitor C13. The parallel connection is followed by the 7th pin, and the 7th pin is connected to the 13th pin through the resistor R13. Connect the first pin of U4, connect the second pin of U5 through resistor Ral, connect the fifth pin|pin of U7, connect the second pin of U8, connect the first pin of U9, the eighth pin passes the resistor. R25 is connected to the 9th pin, the 13th pin is connected to the 14th pin through the resistor R14, and 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, and is connected to the sixth pin through the resistor R2, and the third pin, the fifth pin, the tenth pin, and the twelfth pin. The ground 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 then connected in parallel with Rc23 and capacitor C23. The 7th pin, the 7th pin I is connected to the 2nd bow through the potentiometer R23, the R9 of the resistor is connected to the 9th pin of U1, the second pin of U1 is connected to the potentiometer R12, and the U5 is connected to the U5 by Ra6. 11 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 is connected to the 13th pin through the resistor R33, first connected in parallel with Rc31 and capacitor C31. Connect Rc32 and capacitor C32 in parallel, connect resistor Rc33 and capacitor C33 in parallel and connect to pin 9. Pin 13 is connected to pin 14 through resistor R34. Pin 14 is connected to U3 via potentiometer R32. 2 pin, connected to the 3rd pin of U4;

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 R3, 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 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 left floating, 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 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 Ral, and the first pin is connected through the series of the resistor Ra2 and the diode D4. The resistor Ral and the resistor Ra5 are connected in series to the 6th pin, and the 6th pin is connected via the resistor Ra3. The 3rd pin, the 5th pin, the 10th pin, and the 12th pin are grounded, and the 4th pin is connected to the VCC. The Hth pin is connected to VEE, the 6th pin is connected to the 7th pin through the resistor Ra4, the 7th pin is connected to the 6th pin of U6, the 8th pin is the 4th pin of the U6, and the fourth pin is connected through the resistor Ra9. 9-pin, the 9th pin is connected to the 14th pin through the series connection of the resistor Ra8 and the diode D6, the 13th pin is connected to the 14th pin through the series connection of the resistor Ra7 and the diode D6, and the 14th pin is connected to the 13th pin through the diode D5. Pin

The second pin of the first pin U7 of the analog switch U6, the second pin and the 14th 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 lead of the 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 by the potentiometer R31. 2 pin, 9th pin, 10th pin, U pin, 12th pin, 13th pin is left floating, pin 15 is grounded, The 16th pin is connected to the 13th pin of U7;

The first pin, the sixth pin, the seventh pin I, the eighth pin, the ninth pin, and the 14th pin of the voltage comparator U7 are suspended, and the second pin is connected to the 14V power supply through the resistor R01. Through the series connection of diode D1 and resistor R02, the 13th pin is connected to the positive MV power through the resistor R03, and is connected in series through the diode D2 and the resistor R03;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rsl, and the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, the twelfth pin. Grounding, the 4th bow 1 pin is connected to VCC, the 11th pin is connected to VEE, 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 U9 3 pin, the 9th pin is connected to the 14th pin through the resistor Rs3, and the 13th pin is connected to the 7th pin of the U2;

The first pin of the multiplier U9 is connected to the seventh pin of U1, the third pin is connected to the eighth pin of U8, the second pin, the fourth pin, the sixth pin is grounded, and the fifth pin Connect to VEE, the 7th pin is connected to the 6th pin of U6, and the 8th pin is connected 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, the sixth pin are grounded, and the fifth pin Connect to VEE, the 7th pin is connected to the 4th pin of U6 and the 8th pin is connected to vcc.

2. Four-system automatic switching analog circuit based on L11 type system, which is characterized by: operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 and multiplier U4, multiplier U9 The multiplier U10 is composed of a voltage comparator U7 and an analog switch U6. The operational amplifier U1 is connected to a voltage comparator U7, an operational amplifier U5, an operational amplifier U8, and a multiplier U4. The operational amplifier U2 is connected to an operational amplifier U1 and an operational amplifier. U5, voltage comparator U7, operational amplifier U8, the operational amplifier U3 is connected to the operational amplifier U2, 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 operation The 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, and is connected to the sixth pin through the resistor R1, the third pin, the fifth pin, the Kth pin, and the twelfth pin. 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 Rcll and the capacitor C1 I, and then connected in parallel with the resistor Rcl2 and the capacitor C12, and connected to the resistor RcB and the capacitor C13. Parallel connection to the 7th pin I, the 7th pin is connected to the 13th pin through the resistor RI3, connected to the 1st pin of U4, connected to the 2nd pin of U5 through the resistor Ral, and connected to the 5th pin of U7, Connect the 2nd pin of U8 to the 1st pin of U9, the 8th pin is connected to the 9th pin through the resistor R25, the 13th pin is connected to the 14th pin through the resistor R14, and the 14th pin passes the potentiometer R11 Connect the second pin;

The first pin of the operational amplifier U2 is connected to the second pin through the resistor Ry, and passes through the resistor R2 and the sixth lead. Pin connection, 3rd pin, 5th pin, 10th pin, 12th pin ground, 4th pin is connected to VCC, U pin is connected to VEE, 6th pin is connected with resistor Rc21 and capacitor C21 Parallel connection, then Rc22 and capacitor C22 in parallel, and Rc23 and capacitor C23 in parallel with the seventh pin, the seventh pin is connected to the second pin through the potentiometer R23, through the resistor 24 connected U1 9 pin, connect the second pin of U1 through potentiometer R12, connect the eleventh pin of U5 through Ra6, connect the eleventh pin of U7, connect the thirteenth pin of U8, and connect the first pin of U10, The 8th pin is connected to the 13th pin through the resistor R33, first connected in parallel with Rc31 and capacitor C:31, then connected in parallel with Rc32 and capacitor C32, and connected in parallel with the capacitor Rc33 and capacitor C33, followed by the 9th pin, The 13 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, and is connected to the 3rd pin of U4;

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 R3, and the second pin of the 173 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 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 left floating, and the 11th pin is connected to VEE;

The first pin of the multiplier U4 is connected to the seventh 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 1 pin of the bow is connected to the 2nd pin of U2 through the resistor R21, and the 8th 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 third pin of the UI through the resistor Ral, and the first pin is connected in series through the resistor Ra2 and the diode D4, and the resistor is passed through the resistor. Ral and resistor Ra5 are connected in series to pin 6 and connected to pin 6 through resistor Ra3. Pin 3, pin 5, pin 10, pin 12 are grounded, and pin 4 is connected to VCC. The 11 pin is connected to VEE, the 6th pin is connected to the 7th pin through the resistor Ra4, the 7th pin is connected to the 6th pin of U6, the 8th pin is connected to the 4th pin of U6, and the 9th pin is connected through the resistor Ra9. The pin, the 9th pin is connected through the resistor Ra8 and the diode in series! 4 pin, the 13th pin is connected to the 14th pin through the series connection of the resistor Ra7 and the diode D6, and the 14th pin is connected to the 13th pin through the diode D5;

The second pin of the first pin U7 of the analog switch U6, the second pin and the 14th pin are connected to the positive 14V power supply, the third pin is connected to the negative MV power supply, and the fourth pin is connected to the seventh lead of the 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 by the potentiometer R31. 2 pin, 9th pin, 10th pin, 11 pin, 12th pin, 13th pin is left floating, pin 15 is grounded, pin 16 is connected to pin 13 of U7;

The first pin, the sixth pin, the seventh pin, the eighth pin, the ninth pin, and the J4 pin of the voltage comparator U7 are suspended, and the second pin is connected to the 14V power supply through the resistor R01. Through the series connection of diode D1 and resistor R02, the 13th pin is connected to the 14V power supply through the resistor R03, and is connected in series through the diode D2 and the resistor R03; The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rsl, and the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, the twelfth pin. Ground, the fourth pin is connected to VCC, the eleventh pin is connected to VEE, the sixth pin is connected to the seventh pin through the resistor Rs2, the seventh pin is connected to the third pin of U10, and the eighth pin is connected to the third pin of U9. Pin, the 9th pin is connected to the 14th pin through the resistor Rs3, and the 13th pin is connected to the 7th pin of the U2;

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 The pin is connected to VEE, and the 7th pin is connected to the 4th pin of U6 and the 8th pin is connected to vcc.

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 circuit of the operational amplifier U5.

Figure 5 shows the structure of the peripheral circuits of the operational amplifier U8, multiplier U9 and multiplier U10.

Figure 6 shows the structure of the peripheral circuit of the operational amplifier U3, voltage comparator U7 and analog switch U6.

detailed description

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

Referring to FIG. 1 to FIG. 6, firstly, a LU-type fractional four-system automatic switching chaotic system is constructed, and the system selected by the preferred embodiment is selected.

(1) According to the LU type chaotic system I is - dx l dt = a{y - x)

' fy I dt = -xz + cy 1 a==36, b=3, c=20

(2) According to the LU type chaotic system II is - dx l dt = a(y - x)

' dy I dt = ~xz + cy II a=36, b=3, c=20

(3) According to the chaotic system, the construction of the symbol functions III and IV is -

"i y≥

Sign(y) = IV

-1 j^<0

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

Dxl dt = a{y-x)

Dy I dt = -xz + cy V a=36, b=3, c=20

Dzl dt = xsign(y) - bz

(5) According to the LU type chaotic system VI:

Dxl dt = a(y~x)

Dy I dt = -xz ten VI a=36, b=3, c=20

Dzl dt= ysign{x) - bz

(6) Chaotic system structure selection function VII is:

(7) According to system I, II, V, VI and selection function VII, construct a LU-type four systems to automatically switch chaotic systems IX dxl dt = a{y-x)

Dy / t = -xz + cy IX a=36, b=3, c=20

[dz I dt = f(x )-bz

(8) According to the system I structure - LU type fractional four systems automatically switch chaotic system X

'd ^q xldt ^q = a(yx)

d ^q yl dt ^q = -xz + cy X ( q < l, a=36, b=3, c=20

d ^q zldt ^q =f(xy)-bz

(9) According to the chaotic system X to construct the analog circuit system, use the 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 the analog switch U6. Input, according to x>=0, y>=0, x>0, y<0, x<0, y>=0 and x<0, y<0, different output, realize different output of f(xy) Thus, the chaotic system IX which automatically switches between four systems is realized, and the chaotic system X is realized by fractional integration, the operational amplifier U1, the operational amplifier U2, the operational amplifier U3, the operational amplifier U5, the operational amplifier U8, the LF347, the multiplier U4, Multiplier U9, multiplier U10 uses AD633JN, analog switch U6 uses ADG409, voltage comparator U7 uses LM139;

The first pin of the operational amplifier U1 is connected to the second pin through the resistor Rx, and passes through the resistor R1 and the sixth lead. Pins are connected, the 3rd pin, the 5th pin, the 10th pin, the 12th pin are grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, and the 6th pin is connected to the resistor Rcl l and the capacitor. Parallel connection of C11, reconnecting resistor Rcl2 and capacitor C12 in parallel, and connecting resistor Rcl3 and capacitor C13 in parallel with the 7th pin, 7th pin is connected to the 13th pin through resistor R13, connecting the first bow of U4 The pin is connected to the second pin I of U5 through the resistor Ral, the fifth pin of U7, the second pin of U8, the first pin of U9, and the eighth pin is connected to the ninth pin through resistor R25. The 13th pin is connected to the 14th pin through the resistor R14, and 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, and is connected to the sixth pin through the resistor R2, and the third pin, the fifth pin, the tenth pin, and the twelfth pin The ground 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 then connected in parallel with c23 and capacitor C23. The first pin, the 7th pin is connected to the 2nd pin through the potentiometer R23, the 9th pin of U1 is connected to R24 through the resistor, the 2nd pin of U1 is connected to the second pin of U1 via the potentiometer R12, and the 11th of U5 is connected by Ra6. Pin, connect the 11th pin of U7, connect the 13th pin of U8, connect the 1st pin of U10, the 8th pin is connected to the 13th pin through the resistor R33, first connect Rc31 and capacitor C31 in parallel, then Connect Rc32 and capacitor C32 in parallel, connect resistor Rc33 and capacitor C33 in parallel and connect to pin 9. Pin 13 is connected to pin 14 through resistor R34. Pin 14 is connected to the second pin of U3 via 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, and is connected to the ninth pin of the U2 through the resistor R3, and the second pin of the U3 is connected to the 14 pin of the U2 through the R32. Pin ground, pin 4 to VCC, pin 5, pin 6, pin 7, pin 8, pin 9, pin 10, pin 12, pin 13 The 14th pin is left floating, and the 11th pin is connected to VEE;

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 Ral, and the first pin is connected in series via the resistor Ra2 and the diode D4, and the resistor is passed through the resistor. Ral and resistor Ra5 are connected in series to pin 6 and connected to pin 6 through resistor Ra3. Pin 3, pin 5, pin 10, pin 12 are grounded, and pin 4 is connected to VCC. The 11 pin is connected to VEE, the 6th pin is connected to the 7th pin through the resistor Ra4, the 7th pin is connected to the 6th pin of U6, the 8th pin is connected to the 4th pin of U6, and the 9th pin is connected through the resistor Ra9. Pin, the 9th pin is connected to the W pin through the series connection of the resistor Ra8 and the diode D6, the 13th pin is connected to the 14th pin through the series connection of the resistor Ra7 and the diode D6, and the 14th pin is connected to the 13th pin through the diode D5. ;

The second pin of the first pin U7 of the analog switch U6, the second pin and the 14th pin are connected to a positive 14V power supply. The third pin is connected to the negative 14V power supply, the fourth pin is connected to the third pin of U10, the fifth pin is connected to the eighth pin of U5, the sixth pin is connected to the seventh pin of U9, and the seventh pin is connected. Pin 7 of U5, pin 8 is connected to pin 2 of U3 via potentiometer R31, pin 9, pin 10, pin 11, pin 12, pin 13 is floating, 15 pin ground, the 16th pin is connected to the 13th pin of U7;

The first pin, the sixth pin, the seventh pin, the eighth pin I, the ninth pin, and the 14th pin of the voltage comparator U7 are suspended, and the second pin is connected to the 14V power supply through the resistor R01. Through the series connection of diode D1 and resistor R02, the 13th pin is connected to the 14V power supply through the resistor R03, and is connected in series through the diode D2 and the resistor R03;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rsl, the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, the twelfth pin Ground, the fourth pin is connected to VCC, the eleventh pin is connected to VEE, the sixth pin is connected to the seventh pin through the resistor Rs2, the seventh pin is connected to the third pin of U10, and the eighth pin is connected to the third pin of U9. Pin, the 9th pin passes the resistor Rs; 3 is connected to the 14th pin, and the 13th pin is connected to the 7th pin of U2;

The first pin of the multiplier U9 is connected to the seventh pin I of U1, the third pin is connected to the eighth pin of U8, the second pin, the fourth pin, the sixth pin are grounded, and the fifth lead The pin is connected to VEE, the 7th pin is connected to the 6th pin of U6, and the 8th pin is connected 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, the sixth pin are grounded, and the fifth pin Connected to VEE, the 7th pin is connected to the 4th pin of the U6. The eighth pin is of course not limited by the invention. The present invention is not limited to the above examples, and those skilled in the art are within the scope of the present invention. Variations, modifications, additions or substitutions made within the scope of the invention are also within the scope of the invention.

Claims

Claim

1. A method for automatically switching a chaotic system based on a four-segment system of a U1 type system, characterized in that it comprises the following steps:

(1) According to the U1 type chaotic system I is:

Dxl dt = ay— x)

Dyldt =—xz + cy I a=36, b=3, c=20

Dzldt = \x\-bz

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

II a=36, b=3, c=20

(3) Constructing symbolic functions according to chaotic systems ΠΙ and IV are:

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

Dxl dt = a(y-x)

Dy / dt =—xz + cy a=36, b-3, c=20

[dz / dt = xsign(y)-bz

(5) According to the Ul type chaotic system VI:

[dx I dt = a{y - x)

Dyldt = -xz + cy VI a=36, b=3, c=20

Dzl dt = ysign{x) a bz

(6) According to the chaotic system, the structure selection function VII is

(7) According to the system I, 11, V, VI and the selection function VI I, construct a LU type four system to automatically switch the chaotic system IX Dx l dt = a{y - x)

' dy l dt = -xz + cy IX a=36, b=3, c=20

Dz l dt = f{xy) -bz

(8) Constructing a Lll-type fractional four systems based on system IX to automatically switch chaotic systems X

d ^q xl dt ^q - a{y - x)

' d ^q y I d = -xz + cy X 0<q< 1 , a=36, b=3, c=20

d ^q zl dt ^q = f{xy) -bz

(9) According to the chaotic system X to construct the analog circuit system, the voltage comparator U7 is used to obtain two analog high and low levels, x>=0 or x<0 and y>=0 or y<0, as the control of the analog switch U6. Input, according to x>=0, y>=0, x>0, y<0, x<0, y>=0 and x<0, y<0, different conditions to achieve different output of f (xy) Thus, the chaotic system IX which automatically switches between four systems is realized, and the chaotic system X is realized by fractional integration. The operational amplifier U1, the operational amplifier U2, the operational amplifier U3, the operational amplifier U5, the operational amplifier U8 adopts LF347, the multiplier U4, and the multiplication method. U9, multiplier U10 uses AD633JN, analog switch U6 uses ADG409, voltage comparator U7 uses LM139;

The first pin of the operational amplifier U1 is connected to the first pin through the resistor Rx, and is connected to the sixth pin through the resistor R1, and the third pin, the fifth pin, the tenth pin, and the twelfth pin. The ground is grounded, the fourth pin is connected to VCC, the eleventh pin is connected to VEIi, the sixth pin is connected in parallel with the resistor Rcl l and the capacitor C11, and then the parallel connection of the resistor Rcl2 and the capacitor C12 is connected, and the resistor Rcl 3 and the capacitor C13 are connected. Parallel connection to the 7th pin, the 7th pin is connected to the 13th pin through the resistor R13, connected to the 1st pin of U4, connected to the 2nd pin of U5 through the resistor Ral, connected to the 5th pin of U7, The second pin of U8 is connected to the first pin of U9. The eighth pin is connected to pin 9 through resistor R25. The 13th pin is connected to pin 14 through resistor R14. The 14th pin is connected to potentiometer R11. 2nd pin;

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 through the resistor R2, and the third pin, the fifth pin, the tenth pin, and the twelfth pin The ground 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 then connected in parallel with Rc23 and capacitor C23. The 7th pin, the 7th pin is connected to the 2nd pin via the potentiometer R23, the 9th pin of U1 is connected to R24 through the resistor, the 2nd pin of U1 is connected to the second pin of U1 via the potentiometer R12, and the U5 is connected to the U5 via Ra6. 11-pin, connected to the 11th of the U7 Pin, connect the 13th pin of U8 to the 1st pin of U10, the 8th pin is connected to the 13th pin through the resistor R33, first connected in parallel with Rc31 and capacitor C31, and then connected in parallel with Rc32 and capacitor C32. Connect the resistor Rc33 and the capacitor C33 in parallel with the 9th pin. The 13th pin is connected to the 14th pin through the resistor R34. The 14th pin is connected to the 2nd pin of U3 through the potentiometer R32, and the 3rd pin of U4. Pin

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 R3, and the second pin of the U3 is connected to the 14 pin of the U2 through the R32, the third lead Ground the pin, pin 4 is connected to VCC, pin 5, pin 6, pin 7, pin 8, pin 9, pin 10, pin 12, pin 13 The 14th pin is left floating, and the 11th pin is connected to VEE;

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 Ral, and the first pin is connected in series through the resistor Ra2 and the diode D4, and the resistor is passed through the resistor. Ral and resistor Ra5 are connected in series to pin 6 and connected to pin 6 through resistor Ra3. Pin 3, pin 5, pin 10, pin 12 are grounded, pin 4 is connected to VCC, The 11 pin is connected to VEE, the 6th pin is connected to the 7th pin through the resistor Ra4, the 7th pin is connected to the 6th pin of U6, the 8th pin is connected to the 4th pin of U6, and the 9th pin is connected 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. The 13th pin is connected to the 14th pin through the series connection of the resistor Ra7 and the diode D6, and the 14th pin is connected to the 13th pin through the diode D5. ;

The first pin of the first pin U7 of the analog switch U6, the second pin and the 14th 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 lead of the 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 by the potentiometer R31. 2 pin, 9th pin, 10th pin, 11th pin, 12th pin, 13th pin is left floating, pin 15 is grounded, pin 16 is connected to pin 13 of U7; The first pin, the sixth pin, the seventh pin, the eighth pin, the ninth pin, and the fourteenth pin of the voltage comparator U7 are left floating, and the second pin is connected to the positive 14V power supply through the resistor R01, and the diode is passed through the diode. The series connection of D1 and resistor R02, the 13th pin is connected to the positive 14V power supply through the resistor R03, through the diode Series connection of D2 and resistor R03;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rs l , and the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, the twelfth pin. The ground is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, 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 L9. The third pin, the 9th pin is connected to the 14th pin through the resistor Rs 3, and the 13th pin is connected to the 7th pin of the U2;

The first pin of the multiplier U9 is connected to the seventh pin of U1, the third pin is connected to the eighth pin of U8, the second pin, the fourth pin, the sixth pin are grounded, and the fifth pin Connect to VEE, the 7th pin is connected to the 6th pin of U6, and the 8th pin is connected 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, the sixth pin are grounded, and the fifth pin Connect to VEE, the 7th pin is connected to the 4th pin of U6, the 8th pin is connected to VCC;

2. Four-system automatic switching analog circuit based on LU type system, which is characterized by: operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U5, operational amplifier U8 and multiplier U4, multiplier ϋ9 The multiplier U10 is composed of a voltage comparator U7 and an analog switch U6. The operational amplifier U1 is connected to a voltage comparator U7, an operational amplifier U5, an operational amplifier U8, a multiplier ϋ4, and the operational amplifier U2 is connected to an operational amplifier U1 and an operational amplifier. U5, a voltage comparator 117, an operational amplifier U8, the operational amplifier U3 is connected to an operational amplifier U2, a multiplier U4, the operational amplifier U5 is connected to an analog switch U6, and the voltage comparator U7 is connected to an analog switch U6, the operational amplifier U8 is connected to the operational amplifier U5, the multiplier U9, the multiplier U1 Q, the multiplier U9 is connected to the analog switch ϋ6, 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, and is connected to the sixth pin through the resistor R1, and the third pin, the fifth pin, the tenth pin, and the twelfth pin. The ground 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 Rcl l and the capacitor C11, and then connected in parallel with the resistor Rcl2 and the capacitor C12, and connected to the resistor Rcl 3 and the capacitor C13. And r is connected to the 7th pin, the 7th pin is connected to the 13th pin through the resistor R13, connected to the 1st pin of U4, connected to the 2nd pin of U5 through the resistor Ral, and connected to the 5th pin of U7, Connect the second pin of U8 to the first pin of U9, The 8 pin is connected to the 9th pin through the resistor R25, the 13th pin is connected to the 14th pin through the resistor R14, and 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, and is connected to the sixth pin through the resistor R2, and the third pin, the fifth pin, the tenth pin, and the twelfth pin The ground 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 then connected in parallel with Rc23 and capacitor C23. The 7th pin, the 7th pin is connected to the 2nd pin via the potentiometer R23, the 9th pin of U1 is connected to R24 through the resistor, the 2nd pin of U1 is connected to the second pin of U1 via the potentiometer R12, and the U5 is connected to the U5 via Ra6. 11 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 is connected to the 13th pin through the resistor R33, first connected in parallel with Rc31 and capacitor C31. Connect Rc 32 and capacitor C32 in parallel, and connect resistor Rc 33 and capacitor C33 in parallel with the 9th pin. The 13th pin is connected to the 14th pin through the resistor R34. The 14th pin is connected to the potentiometer R32. 1/3 of the 2nd pin, connected to the 3rd pin of U4;

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 U2 through the resistor R3, and the second pin of U3 is connected to the 14 pin of U2 through R32, the third lead The ground is grounded, the fourth pin is connected to VCC, the fifth pin, the sixth pin, the seventh pin, the eighth pin, the ninth pin, the tenth pin, the twelfth pin, the thirteenth pin, The 14th pin is left floating, and the 11th pin is connected to VEE;

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 Ral, and the first pin is connected in series via the resistor Ra2 and the diode D4, and the resistor is passed through the resistor. Ral and resistor Ra5 are connected in series to pin 6 and connected to pin 6 through resistor Ra 3. Pin 3, pin 5, pin 10, pin 12 are grounded, pin 4 is connected to VCC. The 11th pin is connected to VEE, the 6th pin is connected to the 7th pin through the resistor Ra4, the 7th pin is connected to the 6th pin of U6, the 8th pin is connected to the 4th pin of U6, and the 9th pin is connected to the 9th pin through the resistor Ra9. Pin, the 9th pin is connected to the 14th pin through the series connection of the resistor Ra8 and the diode D6, the 13th pin is connected to the 14th pin through the series connection of the resistor Ra7 and the diode D6, and the 14th pin is connected to the 13th through the diode D5. Pin The second pin of the first pin U7 of the analog switch U6, the second pin and the 14th 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 lead of the 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 by the potentiometer R31. 2 pin, 9th pin, 10th pin, 11th pin, 12th pin, 13th pin is left floating, pin 15 is grounded, pin 16 is connected to pin 13 of U7; The first pin, the sixth pin, the seventh pin, the eighth pin, the ninth pin, and the fourteenth pin of the voltage comparator U7 are left floating, and the second pin is connected to the positive 14V power supply through the resistor R01, and the diode is passed through the diode. The series connection of D1 and resistor R02, the 13th pin is connected to the positive 14V power supply through the resistor R03, and is connected in series through the diode D2 and the resistor R03;

The first pin of the operational amplifier U8 is connected to the sixth pin through the resistor Rs l , and the second pin is connected to the seventh pin of U1, the third pin, the fifth pin, the tenth pin, the twelfth pin. The ground is grounded, the 4th pin is connected to VCC, the 11th pin is connected to VEE, 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 U9 3 pin, the 9th pin is connected to the 14th pin through the resistor Rs 3, and the 13th pin is connected to the 7th pin of U2;

The first pin of the multiplier U9 is connected to the seventh pin of U1, the third pin is connected to the eighth pin of U8, the second pin, the fourth pin, the sixth pin is grounded, the fifth pin Connect to VEE, the 7th pin is connected to the 6th pin of U6, and the 8th pin is connected 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, the sixth pin is grounded, and the fifth pin Connect to VEE, the 7th pin is connected to the 4th pin of U6, the 8th pin is connected to VCC.