CN104202141B - Four-dimensional automatic switchover hyperchaotic system building method based on L ü system and circuit - Google Patents

Abstract

The present invention relates to an automatic switchover hyperchaotic system and circuit, particularly to a four-dimensional automatic switchover hyperchaotic system based on L ü system and circuit, existing hyperchaotic system is usually on the basis of three-dimensional chaotic system, by once increasing one-dimensional variable, and on the variable feedback increased to original three-dimensional chaotic system, form four-dimensional hyperchaotic system, and existing automatically switched chaotic system is usually three-dimensional chaotic system, building method and the circuit with the four-dimensional hyperchaotic system of automatic switching function the most do not propose, in place of this is the deficiencies in the prior art.The present invention is on the basis of three-dimensional L ü chaos system, by the one-dimensional variable of twice increase, and on the variable feedback increased to first equation of three-dimensional L ü chaos system, thus define four-dimensional automatic switchover hyperchaotic system, propose a kind of new method constructing four-dimensional automatic switchover hyperchaotic system, and realized with analog circuit, it is applied to the engineering fields such as communication for four-dimension automatic switchover hyperchaotic system and provides a kind of new selection scheme.

Description

Four-dimensional automatic switchover hyperchaotic system building method based on L ü system and circuit

Technical field

The present invention relates to an automatic switchover hyperchaotic system and circuit, automatically cut particularly to a four-dimension based on L ü system Change hyperchaotic system and circuit.

Background technology

Existing hyperchaotic system is usually on the basis of three-dimensional chaotic system, by once increasing one-dimensional variable, and institute The variable feedback increased in original three-dimensional chaotic system, forms four-dimensional hyperchaotic system, and existing automatically switched chaotic system Being usually three-dimensional chaotic system, building method and the circuit with the four-dimensional hyperchaotic system of automatic switching function the most do not propose, In place of this is the deficiencies in the prior art.The present invention is on the basis of three-dimensional L ü chaos system, by the one-dimensional variable of twice increase, And on the variable feedback increased to first equation of three-dimensional L ü chaos system, thus define four-dimensional automatically switch super mixed Ignorant system, it is proposed that a kind of new method constructing four-dimensional automatic switchover hyperchaotic system, and realized with analog circuit, for Four-dimensional automatic switchover hyperchaotic system is applied to the engineering fields such as communication and provides a kind of new selection scheme.

Summary of the invention

The technical problem to be solved in the present invention is four-dimensional automatic switchover hyperchaotic system building method based on L ü system and circuit, The present invention uses following technological means to realize goal of the invention:

1, four-dimensional automatic switchover hyperchaotic system building method based on L ü system, is characterized in that being, comprises the following steps:

(1) three-dimensional L ü chaos system i is:

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)\\ dy/dt=cy-xz\\ dz/dt=xy-bz\end{array}& i& a=36,b=3,c=20\end{array}\right.$

(2) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=kx, and w is fed back to system i On first equation, it is thus achieved that chaos system ii

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kx\end{array}& ii& a=36,b=3,c=20,k=10\end{array}\right.$

(3) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=ky, and w is fed back to system i On first equation, it is thus achieved that chaos system iii

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=ky\end{array}& iii& a=36,b=3,c=20,k=10\end{array}\right.$

(4) by four-dimensional automatic switchover hyperchaotic system iv of ii and iii structure:

$\begin{array}{cc}\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kf\left(x\right)\end{array}& iv& a=36,b=3,c=20,k=10\end{array}\right.& f\left(x\right)=\left\{\begin{array}{cc}x,& x>0\\ y,& x\≤0\end{array}\right.\end{array}$

(5) according to four-dimensional automatic switchover hyperchaotic system iv constructing analog circuit based on L ü system, utilize operational amplifier U1, Operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and multiplier U5 real Existing multiplying, utilizes operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparative level, as mould Intend the input control signal of switch U6, utilize analog switch U6 to realize the selection output of analogue signal, described operational amplifier U1, operational amplifier U2 and operational amplifier U3 use LF347N, described multiplier U4 and multiplier U5 to use AD633JN, described analog switch U6 use ADG888；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.

2, the analog circuit of four-dimensional automatic switchover hyperchaotic system based on L ü system, is characterized in that being, utilizes computing to put Big device U1, operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and take advantage of Musical instruments used in a Buddhist or Taoist mass U5 realizes multiplying, utilizes operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparison is electric Flat, as the input control signal of analog switch U6, utilize analog switch U6 to realize the selection output of analogue signal, described fortune Calculate amplifier U1, operational amplifier U2 and operational amplifier U3 uses LF347N, described multiplier U4 and multiplier U5 to adopt ADG888 is used with AD633JN, described analog switch U6；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.

Beneficial effect

The present invention is on the basis of three-dimensional L ü chaos system, by the one-dimensional variable of twice increase, and the variable feedback increased On first equation of three-dimensional L ü chaos system, thus define four-dimensional automatic switchover hyperchaotic system, it is proposed that a kind of structure Make the new method of four-dimensional automatic switchover hyperchaotic system, and realized with analog circuit, for four-dimension automatic switchover hyperchaos system System is applied to the engineering fields such as communication and provides a kind of new selection scheme.

Accompanying drawing explanation

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

Fig. 2, Fig. 3 and Fig. 4 are the circuit actual connection figure of the present invention.

Detailed description of the invention

With preferred embodiment, the present invention is further described in detail below in conjunction with the accompanying drawings, sees Fig. 1-Fig. 4.

1, four-dimensional automatic switchover hyperchaotic system building method based on L ü system, is characterized in that being, comprises the following steps:

(1) three-dimensional L ü chaos system i is:

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)\\ dy/dt=cy-xz\\ dz/dt=xy-bz\end{array}& i& a=36,b=3,c=20\end{array}\right.$

(2) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=kx, and w is fed back to system i On first equation, it is thus achieved that chaos system ii

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kx\end{array}& ii& a=36,b=3,c=20,k=10\end{array}\right.$

(3) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=ky, and w is fed back to system i On first equation, it is thus achieved that chaos system iii

$\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=ky\end{array}& iii& a=36,b=3,c=20,k=10\end{array}\right.$

(4) by four-dimensional automatic switchover hyperchaotic system iv of ii and iii structure:

$\begin{array}{cc}\left\{\begin{array}{ccc}\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kf\left(x\right)\end{array}& iv& a=36,b=3,c=20,k=10\end{array}\right.& f\left(x\right)=\left\{\begin{array}{cc}x,& x>0\\ y,& x\≤0\end{array}\right.\end{array}$

(5) according to four-dimension automatic switchover hyperchaotic system v constructing analog Circuits System, operational amplifier U1, operational amplifier are utilized U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and multiplier U5 to realize multiplication fortune Calculate, utilize operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparative level, as analog switch The input control signal of U6, utilizes analog switch U6 to realize the selection output of analogue signal, described operational amplifier U1, computing Amplifier U2 and operational amplifier U3 uses LF347N, described multiplier U4 and multiplier U5 to use AD633JN, described mould Intend switch U6 and use ADG888；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.

2, the analog circuit of four-dimensional automatic switchover hyperchaotic system based on L ü system, is characterized in that being, utilizes computing to put Big device U1, operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and take advantage of Musical instruments used in a Buddhist or Taoist mass U5 realizes multiplying, utilizes operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparison is electric Flat, as the input control signal of analog switch U6, utilize analog switch U6 to realize the selection output of analogue signal, described fortune Calculate amplifier U1, operational amplifier U2 and operational amplifier U3 uses LF347N, described multiplier U4 and multiplier U5 to adopt ADG888 is used with AD633JN, described analog switch U6；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.

Resistance R1=R17=100k Ω, R3=R5=R7=R8=R11=R12=R15=R16=10k Ω in circuit, R2=R4=2.78k Ω, R6=5k Ω, R9=R10=1k Ω, R13=33.3k Ω, R18=80k Ω, C1=C2= C3=C4=10nF.

Certainly, described above not limitation of the present invention, the present invention is also not limited to the example above, the art general Change that logical technical staff is made in the essential scope of the present invention, retrofit, add or replace, fall within the protection of the present invention Scope.

Claims (2)

1. four-dimensional automatic switchover hyperchaotic system building method based on L ü system, is characterized in that being, comprises the following steps:

(1) three-dimensional L ü chaos system i is:

$\left\{\begin{array}{c}dx/dt=a(y-x)\\ dy/dt=cy-xz\\ dz/dt=xy-bz\end{array}\right.---i$ A=36, b=3, c=20

(2) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=kx, and w is fed back to system i On first equation, it is thus achieved that chaos system ii

$\left\{\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kx\end{array}\right.---ii$ A=36, b=3, c=20, k=10

(3) on the basis of three-dimensional L ü chaos system i, increase a differential equation dw/dt=ky, and w is fed back to system i On first equation, it is thus achieved that chaos system iii

$\left\{\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=ky\end{array}\right.---iii$ A=36, b=3, c=20, k=10

(4) by ii and iii a kind of four-dimensional automatic switchover hyperchaotic system iv based on L ü system of structure:

$\left\{\begin{array}{c}dx/dt=a(y-x)+w\\ dy/dt=cy-xz\\ dz/dt=xy-bz\\ dw/dt=kf\left(x\right)\end{array}\right.---iv$ A=36, b=3, c=20, k=10, $f\left(x\right)=\left\{\begin{array}{cc}x,& x>0\\ y,& x\≤0\end{array}\right.$

(5) according to four-dimensional automatic switchover hyperchaotic system iv constructing analog circuit based on L ü system, utilize operational amplifier U1, Operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and multiplier U5 real Existing multiplying, utilizes operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparative level, as mould Intend the input control signal of switch U6, utilize analog switch U6 to realize the selection output of analogue signal, described operational amplifier U1, operational amplifier U2 and operational amplifier U3 use LF347N, described multiplier U4 and U5 to use AD633JN, described Analog switch U6 uses ADG888；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.

2. the analog circuit of four-dimensional automatic switchover hyperchaotic system based on L ü system, is characterized in that being, utilizes operational amplifier U1, operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator, utilize multiplier U4 and multiplier U5 realizes multiplying, utilizes operational amplifier U3 and resistance R17, R18 to constitute comparator, it is thus achieved that a comparative level, As the input control signal of analog switch U6, utilizing analog switch U6 to realize the selection output of analogue signal, described computing is put Big device U1, operational amplifier U2 and operational amplifier U3 use LF347N, described multiplier U4 and U5 to use AD633JN, described analog switch U6 use ADG888；

Described operational amplifier U1 concatenation operation amplifier U2, operational amplifier U3, multiplier U4, multiplier U5 and mould Intend switch U6, described operational amplifier U2 and connect multiplier U4, multiplier U5, analog switch U6 and operational amplifier U1, Described operational amplifier U3 concatenation operation amplifier U1 and analog switch U6, described multiplier U4 concatenation operation amplifier U1 With operational amplifier U2, described multiplier U4 concatenation operation amplifier U1 and operational amplifier U2, described analog switch U6 are even Meet operational amplifier U1；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by resistance R8 and the 6th pin Connecting, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through electric capacity C2 and the 7th pin connect, and the 7th pin meets output y, and the 7th pin is connected by resistance R2 and the 13rd pin, the 7th pin Being connected by resistance R6 and the 2nd pin, the 7th pin connects the 3rd pin of multiplier U5, and the 7th pin meets analog switch U6 The 12nd pin, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects multiplication 1st pin of device U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin meets the 2nd of operational amplifier U3 and draws Foot, the 8th pin connects the 10th pin of analog switch U6, and the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd Pin is connected by resistance R3 and the 14th pin, and the 14th pin is connected by resistance R5 and the 9th pin；

1st pin of described operational amplifier U2 is connected by resistance R16 and the 6th pin, and the 2nd pin passes through resistance R15 Connecting with the 1st pin, the 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th draws Foot is connected by electric capacity C4 and the 7th pin, the 7th pin output w, is drawn with the 13rd of operational amplifier U1 by resistance R1 Foot connects, the 8th pin output z, connects the 3rd pin of multiplier U4, is connected by resistance R13 and the 9th pin, and the 9th Pin is connected by electric capacity C3 and the 8th pin, and the 13rd pin is connected by resistance R11 and the 14th pin, and the 14th pin leads to Cross resistance R12 and the 9th pin connects；

1st pin of the described operational amplifier U3 series connection ground connection by resistance R17 and R18, by resistance R17 and mould The 9th pin intending switch U6 connects, and the 2nd pin connects with the 8th pin of operational amplifier U1, and the 3rd, 5,10,12 Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th, 7,8,9,13,14 pins unsettled；

1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, and the 3rd pin connects the 8th pin of U2, 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin, the 8th pin by resistance R9 Meet VCC；

1st pin of described multiplier U5 connects the 8th foot of operational amplifier U1, and the 3rd pin connects the of operational amplifier U1 7 pins, the 2nd, 4, the 6 equal ground connection of pin, the 5th pin meets VEE, and the 7th pin meets operational amplifier U2 by resistance R10 13rd pin, the 8th pin meets VCC；

1st pin of described analog switch U6 meets VCC, the 2nd, 3,4,5,6,7,8,13,14,15 pins hang Sky, the 10th pin connects with the 8th pin of operational amplifier U1, and the 11st pin is by resistance R14 and operational amplifier U2 The 2nd pin connect, the 12nd pin connects with the 7th pin with operational amplifier U1, the 16th pin ground connection.