CN105071925B - A kind of singly balanced point four wing chaos system circuit containing absolute value - Google Patents

Abstract

The present invention relates to a kind of chaos system and circuit, particularly to a kind of singly balanced point four wing chaos system and circuit containing absolute value.Typical chaos system such as Lorenz system, Chen system and Lu system all have three equilibrium points, wherein having one is zero balancing point, another two is non-zero balancing point, attractor produced by this kind of system is double-wing chaotic attractor, by increasing by four non-zero equilibrium points of method construct of saturation function or continuous function or more equilibrium point on the basis of Typical Chaotic Systems, the chaos system with four wings or multiple wing attractor can be constructed, the present invention is not when increasing saturation function or continuous function, propose a kind of singly balanced point four wing chaos systems containing absolute value, add the type of chaos system, it is applied to engineering practice for chaos system and provides a kind of new selection.

Description

A kind of singly balanced point four wing chaos system circuit containing absolute value

Technical field

The present invention relates to a kind of chaos system and circuit, particularly to a kind of singly balanced point four wing chaos system and circuit containing absolute value.

Background technology

Typical chaos system such as Lorenz system, Chen system and Lu system all have three equilibrium points, wherein having one is zero balancing point, another two is non-zero balancing point, attractor produced by this kind of system is double-wing chaotic attractor, by increasing by four non-zero equilibrium points of method construct of saturation function or continuous function or more equilibrium point on the basis of Typical Chaotic Systems, the chaos system with four wings or multiple wing attractor can be constructed, the present invention is not when increasing saturation function or continuous function, propose a kind of singly balanced point four wing chaos systems containing absolute value, add the type of chaos system, it is applied to engineering practice for chaos system and provides a kind of new selection.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of singly balanced point four wing chaos system circuit containing absolute value, and the present invention adopts following technological means to realize goal of the invention:

A kind of singly balanced point four wing chaos system circuit containing absolute value, it is characterised in that:

$\left\{\begin{array}{c}\frac{dx}{dt}=ax+by+cz\\ \frac{dy}{dt}=-x-\left(f\right(z)-d)y\\ \frac{dz}{dt}=-ex+\left(f\right(y)-d)z\end{array}\right.---i$

In system i formula, a, b, c, d, e is parameter, f (z), and f (y) is nonlinear function；

Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y²Time system i be:

$\left\{\begin{array}{c}\frac{dr}{dt}=2y+z\\ \frac{dy}{dt}=-x-\left(\right|z|-4)y\\ \frac{dz}{dt}=-0.5x+(y^2-4)z\end{array}\right.---ii$

System ii is three-dimensional four wing continuous chaotic system of singly balanced point；

According to system ii constructing analog circuit, operational amplifier U1, operational amplifier U2, operational amplifier U3 and resistance and electric capacity is utilized to constitute anti-phase adder and anti-phase fractional order integrator, operational amplifier U6 and resistance and diode is utilized to constitute absolute value circuit, multiplier U4, multiplier U5 and multiplier U7 is utilized to realize multiplying, described operational amplifier U1, operational amplifier U2, operational amplifier U3 and operational amplifier U6 adopt LF347N, multiplier U4, multiplier U5 and multiplier U7 to adopt AD633JN；

Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation amplifier U1, multiplier U4 and multiplier U7, described operational amplifier U3 concatenation operation amplifier U6 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, described multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；

The 1st of described operational amplifier U1,2 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R12 and the 7 pin, 7th pin meets output-x, connected by the 13rd pin of resistance R18 and operational amplifier U3,8th pin meets output x, connected by the 6th pin of resistance R11 and operational amplifier U1,9th pin is connected by electric capacity C1 and the 8 pin, and the 13rd pin is connected by resistance R9 and the 14 pin, and the 14th pin is connected by resistance R10 and the 9 pin；

The 1st of described operational amplifier U2, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R31 and the 7 pin, 7th pin meets output-y, connect the 3rd pin of multiplier U4, 8th pin meets output y, connected by the 13rd pin of resistance R2 and operational amplifier U1, connected by the 13rd pin of resistance R1 and operational amplifier U2, connected by the 6th pin of resistance R30 and operational amplifier U2, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, 9th pin is connected by electric capacity C2 and the 8 pin, 13rd pin was connected resistance R5 and the 14 pin and was connected, 14th pin is connected by resistance R3 and the 9 pin；

The 1st of described operational amplifier U3, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R14 and the 7 pin, 7th pin meets output-z, connected by the 13rd pin of resistance R8 and operational amplifier U3, 8th pin meets output z, connect the 3rd pin of multiplier U5, connected by the 6th pin of resistance R13 and operational amplifier U3, connected by the 13rd pin of resistance R6 and operational amplifier U1, connected by the 13rd pin of resistance R25 and operational amplifier U6, connected by the 9th pin of resistance R27 and operational amplifier U6, 9th pin is connected by electric capacity C3 and the 8 pin, 13rd pin was connected resistance R15 and the 14 pin and was connected, 14th pin is connected by resistance R16 and the 9 pin；

The 1st of described operational amplifier U6,2,6,7 pins unsettled, 3rd, 5,10,12 pin ground connection, 8th pin connects the 1st pin of multiplier U4,9th pin is connected by resistance R29 and the 8 pin, 13rd pin is connected by resistance R26 and diode D4 and the 14 pin, 13rd pin is connected by resistance R26 and resistance R28 and the 9 pin, and the 14th pin is connected by diode D3 and the 13 pin；

2nd, 4, the 6 equal ground connection of pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R17 and operational amplifier U2, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U5, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R7 and operational amplifier U3, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U7, the 5th pin meets VEE, and the 7th pin connects the 1st pin of multiplier U5, and the 8th pin meets VCC.

The useful fruit of the present invention is: proposes a kind of singly balanced point four wing chaos systems containing absolute value, adds the type of chaos system, is applied to engineering practice for chaos system and provides a kind of new selection.

Accompanying drawing explanation

Fig. 1 is the circuit structure block diagram of the present invention.

Fig. 2 is the actual connection figure of circuit of U1 of the present invention.

Fig. 3 is the actual connection figure of circuit of U2 and U4 of the present invention.

Fig. 4 is the actual connection figure of circuit of U3 of the present invention, U5 and U7.

Fig. 5 is the actual connection figure of circuit of U6 of the present invention.

Fig. 6 is the phasor in y-z direction of the present invention.

Detailed description of the invention

Below in conjunction with accompanying drawing and preferred embodiment, the present invention is further described in detail, referring to Fig. 1-Fig. 6.

A kind of singly balanced point four wing chaos system circuit containing absolute value, it is characterised in that:

$\left\{\begin{array}{c}\frac{dx}{dt}=ax+by+cz\\ \frac{dy}{dt}=-x-\left(f\right(z)-d)y\\ \frac{dz}{dt}=-ex+\left(f\right(y)-d)z\end{array}\right.---i$

In system i formula, a, b, c, d, e is parameter, f (z), and f (y) is nonlinear function；

Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y²Time system i be:

$\left\{\begin{array}{c}\frac{dr}{dt}=2y+z\\ \frac{dy}{dt}=-x-\left(\right|z|-4)y\\ \frac{dz}{dt}=-0.5x+(y^2-4)z\end{array}\right.---ii$

System ii is three-dimensional four wing continuous chaotic system of singly balanced point；

According to system ii constructing analog circuit, operational amplifier U1, operational amplifier U2, operational amplifier U3 and resistance and electric capacity is utilized to constitute anti-phase adder and anti-phase fractional order integrator, operational amplifier U6 and resistance and diode is utilized to constitute absolute value circuit, multiplier U4, multiplier U5 and multiplier U7 is utilized to realize multiplying, described operational amplifier U1, operational amplifier U2, operational amplifier U3 and operational amplifier U6 adopt LF347N, multiplier U4, multiplier U5 and multiplier U7 to adopt AD633JN；

Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation amplifier U1, multiplier U4 and multiplier U7, described operational amplifier U3 concatenation operation amplifier U6 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, described multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；

The 1st of described operational amplifier U1,2 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R12 and the 7 pin, 7th pin meets output-x, connected by the 13rd pin of resistance R18 and operational amplifier U3,8th pin meets output x, connected by the 6th pin of resistance R11 and operational amplifier U1,9th pin is connected by electric capacity C1 and the 8 pin, and the 13rd pin is connected by resistance R9 and the 14 pin, and the 14th pin is connected by resistance R10 and the 9 pin；

The 1st of described operational amplifier U2, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R31 and the 7 pin, 7th pin meets output-y, connect the 3rd pin of multiplier U4, 8th pin meets output y, connected by the 13rd pin of resistance R2 and operational amplifier U1, connected by the 13rd pin of resistance R1 and operational amplifier U2, connected by the 6th pin of resistance R30 and operational amplifier U2, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, 9th pin is connected by electric capacity C2 and the 8 pin, 13rd pin was connected resistance R5 and the 14 pin and was connected, 14th pin is connected by resistance R3 and the 9 pin；

The 1st of described operational amplifier U3, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R14 and the 7 pin, 7th pin meets output-z, connected by the 13rd pin of resistance R8 and operational amplifier U3, 8th pin meets output z, connect the 3rd pin of multiplier U5, connected by the 6th pin of resistance R13 and operational amplifier U3, connected by the 13rd pin of resistance R6 and operational amplifier U1, connected by the 13rd pin of resistance R25 and operational amplifier U6, connected by the 9th pin of resistance R27 and operational amplifier U6, 9th pin is connected by electric capacity C3 and the 8 pin, 13rd pin was connected resistance R15 and the 14 pin and was connected, 14th pin is connected by resistance R16 and the 9 pin；

The 1st of described operational amplifier U6,2,6,7 pins unsettled, 3rd, 5,10,12 pin ground connection, 8th pin connects the 1st pin of multiplier U4,9th pin is connected by resistance R29 and the 8 pin, 13rd pin is connected by resistance R26 and diode D4 and the 14 pin, 13rd pin is connected by resistance R26 and resistance R28 and the 9 pin, and the 14th pin is connected by diode D3 and the 13 pin；

2nd, 4, the 6 equal ground connection of pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R17 and operational amplifier U2, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U5, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R7 and operational amplifier U3, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U7, the 5th pin meets VEE, and the 7th pin connects the 1st pin of multiplier U5, and the 8th pin meets VCC.

Resistance R3=R5=R9=R10=R11=R12=R13=R14=R15=R16=10k Ω in circuit, R25=R26=R27=R29=R30=R31=10k Ω, R1=R8=R28=5k Ω, R7=R17=4K Ω, R2=50K Ω, R18=200K Ω, R4=R6=100K Ω, electric capacity C1=C2=C3=10nF in circuit.

Certainly, described above is not limitation of the present invention, and the present invention is also not limited to the example above, the change made in the essential scope of the present invention of those skilled in the art, remodeling, interpolation or replacement, falls within protection scope of the present invention.

Claims (1)

1. a singly balanced point four wing chaos system circuit containing absolute value, it is characterised in that:

$\left\{\begin{array}{c}\frac{dx}{dt}=ax+by+cz\\ \frac{dy}{dt}=-x-\left(f\right(z)-d)y\\ \frac{dz}{dt}=-ex+\left(f\right(y)-d)z\end{array}\right.---i$

In system i, a, b, c, d, e is parameter, f (z), and f (y) is nonlinear function；

Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y²Time system i be:

$\left\{\begin{array}{c}\frac{x}{dt}=2y+z\\ \frac{dy}{dt}=-x-\left(\right|z|-4)y\\ \frac{dz}{dt}=-0.5x+(y^2-4)z\end{array}\right.---ii$

System ii is three-dimensional four wing continuous chaotic system of singly balanced point；

According to system ii constructing analog circuit, operational amplifier U1, operational amplifier U2, operational amplifier U3 and resistance and electric capacity is utilized to constitute anti-phase adder and anti-phase fractional order integrator, operational amplifier U6 and resistance and diode is utilized to constitute absolute value circuit, multiplier U4, multiplier U5 and multiplier U7 is utilized to realize multiplying, described operational amplifier U1, operational amplifier U2, operational amplifier U3 and operational amplifier U6 adopt LF347N, multiplier U4, multiplier U5 and multiplier U7 to adopt AD633JN；

Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation amplifier U1, multiplier U4 and multiplier U7, described operational amplifier U3 concatenation operation amplifier U6 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, described multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；

The 1st of described operational amplifier U1,2 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R12 and the 7 pin, 7th pin meets output-x, connected by the 13rd pin of resistance R18 and operational amplifier U3,8th pin meets output x, connected by the 6th pin of resistance R11 and operational amplifier U1,9th pin is connected by electric capacity C1 and the 8 pin, and the 13rd pin is connected by resistance R9 and the 14 pin, and the 14th pin is connected by resistance R10 and the 9 pin；

The 1st of described operational amplifier U2, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R31 and the 7 pin, 7th pin meets output-y, connect the 3rd pin of multiplier U4, 8th pin meets output y, connected by the 13rd pin of resistance R2 and operational amplifier U1, connected by the 13rd pin of resistance R1 and operational amplifier U2, connected by the 6th pin of resistance R30 and operational amplifier U2, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, 9th pin is connected by electric capacity C2 and the 8 pin, 13rd pin was connected resistance R5 and the 14 pin and was connected, 14th pin is connected by resistance R3 and the 9 pin；

The 1st of described operational amplifier U3, 2 pins are unsettled, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected by resistance R14 and the 7 pin, 7th pin meets output-z, connected by the 13rd pin of resistance R8 and operational amplifier U3, 8th pin meets output z, connect the 3rd pin of multiplier U5, connected by the 6th pin of resistance R13 and operational amplifier U3, connected by the 13rd pin of resistance R6 and operational amplifier U1, connected by the 13rd pin of resistance R25 and operational amplifier U6, connected by the 9th pin of resistance R27 and operational amplifier U6, 9th pin is connected by electric capacity C3 and the 8 pin, 13rd pin was connected resistance R15 and the 14 pin and was connected, 14th pin is connected by resistance R16 and the 9 pin；

The 1st of described operational amplifier U6,2,6,7 pins unsettled, 3rd, 5,10,12 pin ground connection, 8th pin connects the 1st pin of multiplier U4,9th pin is connected by resistance R29 and the 8 pin, 13rd pin is connected by resistance R26 and diode D4 and the 14 pin, 13rd pin is connected by resistance R26 and resistance R28 and the 9 pin, and the 14th pin is connected by diode D3 and the 13 pin；

2nd, 4, the 6 equal ground connection of pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R17 and operational amplifier U2, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U5, the 5th pin meets VEE, and the 7th pin is connected by the 13rd pin of resistance R7 and operational amplifier U3, and the 8th pin meets VCC；

2nd, 4, the 6 equal ground connection of pin of described multiplier U7, the 5th pin meets VEE, and the 7th pin connects the 1st pin of multiplier U5, and the 8th pin meets VCC.