CN104202144B - The analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system - Google Patents

Abstract

nullThe present invention provides a kind of hyperchaotic system of the four-dimension without equilibrium point based on three-dimensional Rikitake chaos system and analog circuit，Utilize operational amplifier U1、Operational amplifier U2 and resistance and electric capacity constitute anti-phase adder and inverting integrator，Utilize multiplier U3、U4 and U5 realizes multiplying，1V DC source is utilized to realize constant inflow，Described operational amplifier U1 and operational amplifier U2 uses LF347N，Described multiplier U3、U4 and U5 uses AD633JN,Described operational amplifier U1 concatenation operation amplifier U2、Multiplier U3 and multiplier U4，Described operational amplifier U2 connects multiplier U5、DC source and operational amplifier U1，Described multiplier U3 concatenation operation amplifier U1，Described multiplier U4 concatenation operation amplifier U1，Described multiplier U5 concatenation operation amplifier U2，Described 1V DC source concatenation operation amplifier U2，The present invention is on the basis of three-dimensional Rikitake chaos system，Propose a four-dimensional hyperchaotic system without equilibrium point，And realized with analog circuit，It is applied to the engineering fields such as communication for chaos system and provides a kind of new method and thinking.

Description

The analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system

Technical field

The present invention relates to a chaos system and analog circuit, particularly to a nothing based on three-dimensional Rikitake chaos system Equilibrium point four-dimension hyperchaotic system and analog circuit.

Background technology

At present, the hyperchaotic system that oneself has is usually on the basis of the three-dimensional chaotic system with three equilibrium points, increases by one Dimension, forms the four-dimensional hyperchaotic system with an at least equilibrium point, and the four-dimensional hyperchaotic system without equilibrium point is not the most carried Going out, the present invention is on the basis of three-dimensional Rikitake chaos system, it is proposed that a four-dimensional hyperchaotic system without equilibrium point, and Realized with analog circuit, be applied to the engineering fields such as communication for chaos system and provide a kind of new method and thinking.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of system of hyperchaos without equilibrium point based on three-dimensional Rikitake chaos system The analog circuit of system, the present invention uses following technological means to realize goal of the invention:

1, the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system, is characterized in that being, comprises the following steps:

(1) Rikitake three-dimensional chaotic system i is:

$\left\{\begin{array}{ccc}dx/dt=-\mathrm{\μ}x+yz& & \\ dy/dt=-\mathrm{\μ}y+(z-a)x& i& \mathrm{\μ}=2,a=5\\ dz/dt=1-xy& & \end{array}\right.$

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

$\left\{\begin{array}{ccc}dx/dt=-\mathrm{\μ}x+yz& & \\ \begin{array}{c}dy/dt=-\mathrm{\μ}y+(z-a)x+w\\ dz/dt=1-xy\end{array}& ii& \mathrm{\μ}=2,a=40,k=3\\ dw/dt=-ky& & \end{array}\right.$

(3) according to without equilibrium point hyperchaotic system ii constructing analog Circuits System, operational amplifier U1, U2 and resistance and electricity are utilized Hold and constitute anti-phase adder and inverting integrator, utilize multiplier U3, U4 and U5 to realize multiplying, utilize 1V unidirectional current Source realizes constant inflow, and described operational amplifier U1 and operational amplifier U2 uses LF347N, described multiplier U3, U4 and U5 uses AD633JN；

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connection are taken advantage of Musical instruments used in a Buddhist or Taoist mass U5,1V DC source and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 Concatenation operation amplifier U1, described multiplier U5 concatenation operation amplifier U2, described 1V DC source concatenation operation amplifier U2；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by the 6th of resistance R8 Yu U1 the Pin connects, the 3rd, 5,10,12 pin ground connection, and the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through 7th pin of electric capacity C2 with U1 connects, and the 7th pin meets output y, and the 7th pin passes through resistance R10 and the 6th pin phase Connecing, the 7th pin is connected by the 6th pin of resistance R13 with U2, and the 7th pin connects the 1st pin of multiplier U3, and the 7th Pin meets the 3rd pin of multiplier U5, the 8th pin output x, and the 8th pin is connected by electric capacity C1 and the 9th pin, 8th pin connects the 1st pin of multiplier U4, and the 8th pin connects the 1st pin of multiplier U5, and the 8th pin passes through resistance 6th pin of R9 with U1 connects, and the 8th pin is connected by the 9th pin of resistance R4 with U1, and the 13rd pin is by electricity Resistance R2 and the 14th pin connect, and the 14th pin is connected by resistance R3 and the 9th pin；

The 1st of described operational amplifier U2,2,13,14 pins unsettled, the 3rd, 5,10,12 pin ground connection, the 4th draws Foot meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by electric capacity C4 and the 7th pin, the 7th pin output w, logical The 2nd pin crossing resistance R5 with U1 connects, and the 8th pin meets output z, connects the 3rd pin of multiplier U3, connects multiplier 3rd pin of U4, the 9th pin is connected by the 8th pin of electric capacity C3 with U2, connects 1V power supply by resistance R12 and is followed by Ground；

1st pin of described multiplier U3 connects the 7th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R1, and the 8th pin meets VCC；

1st pin of described multiplier U4 connects the 8th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R6, and the 8th pin meets VCC.

1st pin of described multiplier U5 connects the 8th foot of U1, and the 3rd pin connects the 7th pin of U1, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R11, and the 8th pin meets VCC.

2, the analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on three-dimensional chaotic system, is characterized in that being, by computing Amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC source composition；

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connection are taken advantage of Musical instruments used in a Buddhist or Taoist mass U5, DC source and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 are even Connect operational amplifier U1, described multiplier U5 concatenation operation amplifier U2, described 1V DC source concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 use LF347D, and described multiplier U3, U4 and U5 use AD633JN；

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 R10 and the 6th pin, the 7th pin Being connected by the 6th pin of resistance R13 with U2, the 7th pin connects the 1st pin of multiplier U3, and the 7th pin connects multiplier 3rd pin of U5, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects to be taken advantage of 1st pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin passes through resistance R9 and the 6th pin Connecting, the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd pin is connected by resistance R2 and the 14th pin, 14th pin is connected by resistance R3 and the 9th pin；

The 1st of described operational amplifier U2,2,13,14 pins unsettled, the 3rd, 5,10,12 pin ground connection, the 4th draws Foot meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by electric capacity C4 and the 7th pin, the 7th pin output w, logical The 2nd pin crossing resistance R5 with U1 connects, and the 8th pin meets output z, connects the 3rd pin of multiplier U3, connects multiplier 3rd pin of U4, the 9th pin is connected by electric capacity C3 and the 8th pin, connects ground connection after 1V power supply by resistance R12；

1st pin of described multiplier U3 connects the 7th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R1, and the 8th pin meets VCC；

1st pin of described multiplier U4 connects the 8th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R6, and the 8th pin meets VCC；

1st pin of described multiplier U5 connects the 8th foot of U1, and the 3rd pin connects the 7th pin of U1, the 2nd, 4,6 pins equal Ground connection, the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R11, and the 8th pin meets VCC；

The useful fruit of the present invention is: on the basis of three-dimensional Rikitake chaos system, it is proposed that the four-dimension without equilibrium point Hyperchaotic system, and being realized with analog circuit, is applied to the engineering fields such as communication and provides a kind of new for chaos system Method and thinking.

Accompanying drawing explanation

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

Fig. 2 and Fig. 3 is 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. 3.

1, the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system, is characterized in that being, comprises the following steps:

(1) Rikitake three-dimensional chaos chaos system i is:

$\left\{\begin{array}{ccc}dx/dt=-\mathrm{\μ}x+yz& & \\ dy/dt=-\mathrm{\μ}y+(z-a)x& i& \mathrm{\μ}=2,a=5\\ dz/dt=1-xy& & \end{array}\right.$

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

$\left\{\begin{array}{ccc}dx/dt=-\mathrm{\μ}x+yz& & \\ \begin{array}{c}dy/dt=-\mathrm{\μ}y+(z-a)x+w\\ dz/dt=1-xy\end{array}& ii& \mathrm{\μ}=2,a=40,k=3\\ dw/dt=-ky& & \end{array}\right.$

(3) according to without equilibrium point hyperchaotic system ii constructing analog Circuits System, operational amplifier U1, U2 and resistance and electricity are utilized Hold and constitute anti-phase adder and inverting integrator, utilize multiplier U3, U4 and U5 to realize multiplying, utilize 1V unidirectional current Source realizes constant inflow, and described operational amplifier U1 and operational amplifier U2 uses LF347N, described multiplier U3, U4 and U5 uses AD633JN；

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connection are taken advantage of Musical instruments used in a Buddhist or Taoist mass U5,1V DC source and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 Concatenation operation amplifier U1, described multiplier U5 concatenation operation amplifier U2, described 1V DC source concatenation operation amplifier U2；

1st pin of described operational amplifier U1 is connected by resistance R7 and the 2nd pin, by the 6th of resistance R8 Yu U1 the Pin connects, the 3rd, 5,10,12 pin ground connection, and the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin passes through 7th pin of electric capacity C2 with U1 connects, and the 7th pin meets output y, and the 7th pin passes through resistance R10 and the 6th pin phase Connecing, the 7th pin is connected by the 6th pin of resistance R13 with U2, and the 7th pin connects the 1st pin of multiplier U3, and the 7th Pin meets the 3rd pin of multiplier U5, the 8th pin output x, and the 8th pin is connected by electric capacity C1 and the 9th pin, 8th pin connects the 1st pin of multiplier U4, and the 8th pin connects the 1st pin of multiplier U5, and the 8th pin passes through resistance 6th pin of R9 with U1 connects, and the 8th pin is connected by the 9th pin of resistance R4 with U1, and the 13rd pin is by electricity Resistance R2 and the 14th pin connect, and the 14th pin is connected by resistance R3 and the 9th pin；

The 1st of described operational amplifier U2,2,13,14 pins unsettled, the 3rd, 5,10,12 pin ground connection, the 4th draws Foot meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by electric capacity C4 and the 7th pin, the 7th pin output w, logical The 2nd pin crossing resistance R5 with U1 connects, and the 8th pin meets output z, connects the 3rd pin of multiplier U3, connects multiplier 3rd pin of U4, the 9th pin is connected by the 8th pin of electric capacity C3 with U2, connects 1V power supply by resistance R12 and is followed by Ground；

1st pin of described multiplier U3 connects the 7th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R1, and the 8th pin meets VCC；

1st pin of described multiplier U4 connects the 8th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R6, and the 8th pin meets VCC；

1st pin of described multiplier U5 connects the 8th foot of U1, and the 3rd pin connects the 7th pin of U1, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R11, and the 8th pin meets VCC.

2, the analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system, is characterized in that being, by transporting Calculate amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC source composition；

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connection are taken advantage of Musical instruments used in a Buddhist or Taoist mass U5, DC source and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 are even Connect operational amplifier U1, described multiplier U5 concatenation operation amplifier U2, described 1V DC source concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 use LF347D, and described multiplier U3, U4 and U5 use AD633JN；

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 R10 and the 6th pin, the 7th pin Being connected by the 6th pin of resistance R13 with U2, the 7th pin connects the 1st pin of multiplier U3, and the 7th pin connects multiplier 3rd pin of U5, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects to be taken advantage of 1st pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin passes through resistance R9 and the 6th pin Connecting, the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd pin is connected by resistance R2 and the 14th pin, 14th pin is connected by resistance R3 and the 9th pin；

The 1st of described operational amplifier U2,2,13,14 pins unsettled, the 3rd, 5,10,12 pin ground connection, the 4th draws Foot meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by electric capacity C4 and the 7th pin, the 7th pin output w, logical The 2nd pin crossing resistance R5 with U1 connects, and the 8th pin meets output z, connects the 3rd pin of multiplier U3, connects multiplier 3rd pin of U4, the 9th pin is connected by electric capacity C3 and the 8th pin, connects ground connection after 1V power supply by resistance R12；

1st pin of described multiplier U3 connects the 7th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R1, and the 8th pin meets VCC；

1st pin of described multiplier U4 connects the 8th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R6, and the 8th pin meets VCC；

1st pin of described multiplier U5 connects the 8th foot of U1, and the 3rd pin connects the 7th pin of U1, the 2nd, 4,6 pins equal Ground connection, the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R11, and the 8th pin meets VCC.

Resistance R1=R2=R3=R6=R7=R8=R9=R11=10k Ω, R4=R10=50k Ω in circuit, R5=R12=100k Ω, R13=33.33k 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 (1)

1. the analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system, is characterized in that being, by transporting Calculate amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC source composition；

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connection are taken advantage of Musical instruments used in a Buddhist or Taoist mass U5, DC source and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 are even Connect operational amplifier U1, described multiplier U5 concatenation operation amplifier U2, described 1V DC source concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 use LF347D, and described multiplier U3, U4 and U5 use AD633JN；

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 R10 and the 6th pin, the 7th pin Being connected by the 6th pin of resistance R13 with U2, the 7th pin connects the 1st pin of multiplier U3, and the 7th pin connects multiplier 3rd pin of U5, the 8th pin output x, the 8th pin is connected by electric capacity C1 and the 9th pin, and the 8th pin connects to be taken advantage of 1st pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin connects the 1st pin of multiplier U5, and the 8th pin passes through resistance R9 and the 6th pin Connecting, the 8th pin is connected by resistance R4 and the 9th pin, and the 13rd pin is connected by resistance R2 and the 14th pin, 14th pin is connected by resistance R3 and the 9th pin；

The 1st of described operational amplifier U2,2,13,14 pins unsettled, the 3rd, 5,10,12 pin ground connection, the 4th draws Foot meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by electric capacity C4 and the 7th pin, the 7th pin output w, logical The 2nd pin crossing resistance R5 with U1 connects, and the 8th pin meets output z, connects the 3rd pin of multiplier U3, connects multiplier 3rd pin of U4, the 9th pin is connected by electric capacity C3 and the 8th pin, connects ground connection after 1V power supply by resistance R12；

1st pin of described multiplier U3 connects the 7th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R1, and the 8th pin meets VCC；

1st pin of described multiplier U4 connects the 8th foot of U1, and the 3rd pin connects the 8th pin of U2, and the 2nd, 4,6 draw The equal ground connection of foot, the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R6, and the 8th pin meets VCC；

1st pin of described multiplier U5 connects the 8th foot of U1, and the 3rd pin connects the 7th pin of U1, the 2nd, 4,6 pins equal Ground connection, the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R11, and the 8th pin meets VCC.