CN104468082B - The construction method of the Lorenz type hyperchaotic system containing y side based on memristor - Google Patents

Abstract

nullThe present invention relates to construction method and the circuit of a kind of Lorenz type hyperchaotic system containing y side based on memristor，Utilize operational amplifier U1、Operational amplifier U2、Operational amplifier U3 and resistance、Electric capacity realizes addition、Anti-phase and integral operation，Utilize multiplier U4、The multiplying in system is realized with multiplier U5，Operational amplifier U6 and multiplier U7 and multiplier U8 is utilized to realize the memristor model in the present invention，Operational amplifier U1 concatenation operation amplifier U2、Operational amplifier U6 and multiplier U4、Multiplier U5、Multiplier U8，Operational amplifier U2 concatenation operation amplifier U3 and multiplier U4，Operational amplifier U3 connects multiplier U5，Operational amplifier U6 connects multiplier U7 and multiplier U8，Multiplier U7 connects multiplier U8，The present invention is on the basis of the Lorenz type chaos system containing y side，A memristor element is utilized to increase the four-dimensional hyperchaotic system of one-dimensional composition，Propose memristor and be applied to the new method of hyperchaotic system.

Description

The construction method of the Lorenz type hyperchaotic system containing y side based on memristor

Technical field

The present invention relates to a kind of chaos system and circuit realiration, particularly to a kind of Lorenz type containing y side based on memristor The construction method of hyperchaotic system.

Background technology

Currently, the method constructing four dimension ultra-chaos is mainly on the basis of three-dimensional chaotic system, increases the one-dimensional composition four-dimension super Chaos system, memristor, as the newfound physical component in HP Lab in 2008, can substitute for the Cai Shi in cai's circuit Diode constitutes four dimensional chaos system, and in cai's circuit, hyperchaos to be constituted then needs 2 memristor elements, it is therefore desirable to five dimensions Or five above systems of dimension, the circuit system realizing hyperchaos in the four-dimensional system with memristor element is the most fewer, memristor The method being applied to four-dimensional hyperchaotic system is not the most suggested, in place of this is the deficiencies in the prior art.

Summary of the invention

The technical problem to be solved in the present invention is to provide the structure of a kind of Lorenz type hyperchaotic system containing y side based on memristor Construction method:

The construction method of the Lorenz type hyperchaotic system containing y side based on memristor, comprises the following steps:

(1) the Lorenz type chaos system i containing y side is:

$\left\{\begin{array}{c}dx/dt=a(y-x)\\ \begin{array}{cc}dy/dt=bx-y-xz& a=10,b=30,c=8/3\end{array}\\ dz/dt=y^2-cz\end{array}\right.---\left(i\right)$

X in formula, y, z are state variable；

(2) memristor that the present invention uses is that magnetic control memristor model ii is:

WhereinRepresent magnetic control memristor,Representing magnetic flux, m, n are greater than the parameter of zero；

(3) the magnetic control memristor model derivation to ii must be recalled and leads device model iii and be:

Representing that magnetic control is recalled to lead, m, n are greater than the parameter of zero；

(4) magnetic control is recalled lead device model iii as unidimensional system variable, be added in the second equation of Lorenz type chaos system containing y side On, it is thus achieved that a kind of Lorenz type hyperchaotic system iv containing y side based on memristor:

$\left\{\begin{array}{c}dx/dt=a\left(y-x\right)\\ dy/dt=bx-y-xz-kxW\left(u\right)\\ dz/dt=y^2-cz\\ du/dt=-x\end{array}\right.---iv$

X in formula, y, z, u are state variable, parameter value a=10, b=30, c=8/3, m=8, n=0.004, k=3；

(5) circuit based on system iv structure, utilizes operational amplifier U1, operational amplifier U2, operational amplifier U3 and electricity Resistance, electric capacity realize addition, anti-phase and integral operation, utilize the multiplication fortune that multiplier U4 and multiplier U5 realizes in system Calculate, utilize operational amplifier U6 and multiplier U7, multiplier U8 and electric capacity to realize the memristor model in the present invention, described Operational amplifier U1, U2 and U3 use LF347BN, and described multiplier U4, U5, U7 and U8 use AD633JN, described operational amplifier U6 use LF353N；

1st pin of described operational amplifier U1 connects the 2nd pin by resistance Cx, connects the 6th by resistance R2 and draws Foot, connects the 13rd pin of operational amplifier U2 by resistance Ry1, the 3rd pin, the 5th pin, the 10th pin, the 12nd Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through Resistance R3 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rx1, connects computing by memristor Ry4 and puts 13rd pin of big device U2, the 7th pin is directly connected to the 1st pin of multiplier U4, and the 13rd pin is by resistance Rx even Connecing the 14th pin, the 14th pin connects the 2nd pin by resistance R1；

1st pin of described operational amplifier U2, the 2nd pin, the 6th pin, the 7th pin are unsettled, the 3rd pin, 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin leads to Cross resistance Ry2 and connect the 13rd pin, connect the 13rd pin of operational amplifier U1 by resistance Rx2, connect by electric capacity Cy 9 pins, the 8th pin is directly connected to the 1st pin and the 3rd pin of multiplier U5, and the 13rd pin connects by resistance Ry 14 pins, the 14th pin connects the 9th pin by resistance R4；

1st pin of described operational amplifier U3 connects the 2nd pin by electric capacity Cz, connects the 6th pin by resistance R6, 1st pin is directly connected to the 3rd pin of multiplier U4, and the 3rd pin, the 5th pin, the 10th pin, the 12nd pin connect Ground, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through resistance R7 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rz2, and the 13rd pin connects the 14th by resistance Rz and draws Foot, the 14th pin connects the 2nd pin by resistance R5；

7th pin of the 1st pin concatenation operation amplifier U1 of described multiplier U4, the 2nd pin, the 4th pin, 6 pin ground connection, the 1st pin of the 3rd pin concatenation operation amplifier U3, the 5th pin meets VEE, and the 8th pin connects VCC, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance Ry3；

1st pin of described multiplier U5 and the 8th pin of the 3rd pin concatenation operation amplifier U2, the 2nd pin, 4 pins, the 6th pin ground connection, the 5th pin meets VEE, and the 8th pin meets VCC, and the 7th pin connects fortune by resistance Rz1 Calculate the 13rd pin of amplifier U3.

Described magnetic control is recalled and is led device and realized by operational amplifier U6 and multiplier U7 and multiplier U8, and described operational amplifier U6 connects Operational amplifier U1 and multiplier U7 and multiplier U8, multiplier U7 connect multiplier U8, multiplier U8 concatenation operation Amplifier U2；

1st pin of described operational amplifier U6, the 2nd pin, the 3rd pin are unsettled, and the 4th pin meets VEE, and the 5th Pin ground connection, the 6th pin connects the 7th pin by electric capacity C4, draws by the 7th of resistance R8 concatenation operation amplifier U1 the Foot, the 7th pin is directly connected to the 1st pin and the 3rd pin of multiplier U7, and the 8th pin meets VCC；

1st pin of described multiplier U7 and the 7th pin of the 3rd pin concatenation operation amplifier U6, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin connects the 3rd pin of multiplier U8, the 8th pin Meet VCC；

1st pin of described multiplier U8 connects the 6th pin of operational amplifier U6 by resistance R8, by resistance R10 With series connection the 7th pin of resistance R9, the 1st pin is directly connected to the 7th pin of operational amplifier U1, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin meets the of operational amplifier U2 by resistance R9 13 pins, the 8th pin meets VCC.

Beneficial effect: the present invention, on the basis of the Lorenz type chaos system containing y side, utilizes a memristor element to increase by one Dimension constitutes four-dimensional hyperchaotic system, it is proposed that memristor is applied to the new method of hyperchaotic system.

Accompanying drawing explanation

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

Fig. 2 is to realize in the present invention recalling the circuit actual connection figure leading device.

Fig. 3 is the circuit actual connection figure of operational amplifier U1.

Fig. 4 is the circuit actual connection figure of multiplier U4 and operational amplifier U2.

Fig. 5 is the circuit actual connection figure of multiplier U5 and operational amplifier U3.

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. 5.

The construction method of the Lorenz type hyperchaotic system containing y side based on memristor, comprises the following steps:

(1) the Lorenz type chaos system i containing y side is:

$\left\{\begin{array}{c}dx/dt=a(y-x)\\ \begin{array}{cc}dy/dt=bx-y-xz& a=10,b=30,c=8/3\end{array}\\ dz/dt=y^2-cz\end{array}\right.---\left(i\right)$

X in formula, y, z are state variable；

(2) memristor that the present invention uses is that magnetic control memristor model ii is:

WhereinRepresent magnetic control memristor,Representing magnetic flux, m, n are greater than the parameter of zero；

(3) the magnetic control memristor model derivation to ii must be recalled and leads device model iii and be:

Representing that magnetic control is recalled to lead, m, n are greater than the parameter of zero；

(4) magnetic control is recalled lead device model iii as unidimensional system variable, be added in the second equation of Lorenz type chaos system containing y side On, it is thus achieved that a kind of Lorenz type hyperchaotic system iv containing y side based on memristor:

$\left\{\begin{array}{c}dx/dt=a\left(y-x\right)\\ dy/dt=bx-y-xz-kxW\left(u\right)\\ dz/dt=y^2-cz\\ du/dt=-x\end{array}\right.---iv$

X in formula, y, z, u are state variable, parameter value a=10, b=30, c=8/3, m=8, n=0.004, k=3；

(5) circuit based on system iv structure, utilizes operational amplifier U1, operational amplifier U2, operational amplifier U3 and electricity Resistance, electric capacity realize addition, anti-phase and integral operation, utilize the multiplication fortune that multiplier U4 and multiplier U5 realizes in system Calculate, utilize operational amplifier U6 and multiplier U7, multiplier U8 and electric capacity to realize the memristor model in the present invention, described Operational amplifier U1, U2 and U3 use LF347BN, and described multiplier U4, U5, U7 and U8 use AD633JN, described operational amplifier U6 use LF353N；

1st pin of described operational amplifier U1 connects the 2nd pin by resistance Cx, connects the 6th by resistance R2 and draws Foot, connects the 13rd pin of operational amplifier U2 by resistance Ry1, the 3rd pin, the 5th pin, the 10th pin, the 12nd Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through Resistance R3 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rx1, connects computing by memristor Ry4 and puts 13rd pin of big device U2, the 7th pin is directly connected to the 1st pin of multiplier U4, and the 13rd pin is by resistance Rx even Connecing the 14th pin, the 14th pin connects the 2nd pin by resistance R1；

1st pin of described operational amplifier U2, the 2nd pin, the 6th pin, the 7th pin are unsettled, the 3rd pin, 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin leads to Cross resistance Ry2 and connect the 13rd pin, connect the 13rd pin of operational amplifier U1 by resistance Rx2, connect by electric capacity Cy 9 pins, the 8th pin is directly connected to the 1st pin and the 3rd pin of multiplier U5, and the 13rd pin connects by resistance Ry 14 pins, the 14th pin connects the 9th pin by resistance R4；

1st pin of described operational amplifier U3 connects the 2nd pin by electric capacity Cz, connects the 6th pin by resistance R6, 1st pin is directly connected to the 3rd pin of multiplier U4, and the 3rd pin, the 5th pin, the 10th pin, the 12nd pin connect Ground, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through resistance R7 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rz2, and the 13rd pin connects the 14th by resistance Rz and draws Foot, the 14th pin connects the 2nd pin by resistance R5；

7th pin of the 1st pin concatenation operation amplifier U1 of described multiplier U4, the 2nd pin, the 4th pin, 6 pin ground connection, the 1st pin of the 3rd pin concatenation operation amplifier U3, the 5th pin meets VEE, and the 8th pin connects VCC, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance Ry3；

1st pin of described multiplier U5 and the 8th pin of the 3rd pin concatenation operation amplifier U2, the 2nd pin, 4 pins, the 6th pin ground connection, the 5th pin meets VEE, and the 8th pin meets VCC, and the 7th pin connects fortune by resistance Rz1 Calculate the 13rd pin of amplifier U3.

Described magnetic control is recalled and is led device and realized by operational amplifier U6 and multiplier U7 and multiplier U8, and described operational amplifier U6 connects Operational amplifier U1 and multiplier U7 and multiplier U8, multiplier U7 connect multiplier U8, multiplier U8 concatenation operation Amplifier U2；

1st pin of described operational amplifier U6, the 2nd pin, the 3rd pin are unsettled, and the 4th pin meets VEE, and the 5th Pin ground connection, the 6th pin connects the 7th pin by electric capacity C4, draws by the 7th of resistance R8 concatenation operation amplifier U1 the Foot, the 7th pin is directly connected to the 1st pin and the 3rd pin of multiplier U7, and the 8th pin meets VCC；

1st pin of described multiplier U7 and the 7th pin of the 3rd pin concatenation operation amplifier U6, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin connects the 3rd pin of multiplier U8, the 8th pin Meet VCC；

1st pin of described multiplier U8 connects the 6th pin of operational amplifier U6 by resistance R8, by resistance R10 With series connection the 7th pin of resistance R9, the 1st pin is directly connected to the 7th pin of operational amplifier U1, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin meets the of operational amplifier U2 by resistance R9 13 pins, the 8th pin meets VCC.

Certainly, described above not restriction to invention, the present invention is also not limited to the example above, the art common Change that technical staff is made in the essential scope of the present invention, retrofit, add or replace, fall within the protection model of the present invention Enclose.

Claims (2)

1. the construction method of the Lorenz type hyperchaotic system containing y side based on memristor, it is characterised in that comprise the following steps:

(1) the Lorenz type chaos system i containing y side is:

$\left\{\begin{array}{cc}\begin{array}{c}dx/dt=a\left(y-x\right)\\ dy/dt=bx-y-xz\\ dz/dt=y^2-cz\end{array}& a=10,b=30,c=8/3\end{array}\right.---i$

X in formula, y, z are state variable；

(2) memristor that the present invention uses is that magnetic control memristor model ii is:

WhereinRepresent magnetic control memristor,Representing magnetic flux, m, n are greater than the parameter of zero；

(3) the magnetic control memristor model derivation to ii must be recalled and leads device model iii and be:

Representing that magnetic control is recalled to lead, m, n are greater than the parameter of zero；

(4) magnetic control is recalled lead device model iii as unidimensional system variable, be added in the second equation of Lorenz type chaos system containing y side On, it is thus achieved that a kind of Lorenz type hyperchaotic system iv containing y side based on memristor:

$\left\{\begin{array}{c}dx/dt=a\left(y-x\right)\\ dy/dt=bx-y-xz-kxW\left(u\right)\\ dz/dt=y^2-cz\\ du/dt=-x\end{array}\right.---iv$

X in formula, y, z, u are state variable, parameter value a=10, b=30, c=8/3, m=8, n=0.004, k=3；

(5) circuit based on system iv structure, utilizes operational amplifier U1, operational amplifier U2, operational amplifier U3 and electricity Resistance, electric capacity realize addition, anti-phase and integral operation, utilize the multiplication fortune that multiplier U4 and multiplier U5 realizes in system Calculate, utilize operational amplifier U6 and multiplier U7, multiplier U8 and electric capacity to realize the memristor model in the present invention, described Operational amplifier U1, U2 and U3 use LF347BN, and described multiplier U4, U5, U7 and U8 use AD633JN, described operational amplifier U6 use LF353N；

1st pin of described operational amplifier U1 connects the 2nd pin by resistance Cx, connects the 6th by resistance R2 and draws Foot, connects the 13rd pin of operational amplifier U2 by resistance Ry1, the 3rd pin, the 5th pin, the 10th pin, the 12nd Pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through Resistance R3 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rx1, connects computing by memristor Ry4 and puts 13rd pin of big device U2, the 7th pin is directly connected to the 1st pin of multiplier U4, and the 13rd pin is by resistance Rx even Connecing the 14th pin, the 14th pin connects the 2nd pin by resistance R1；

1st pin of described operational amplifier U2, the 2nd pin, the 6th pin, the 7th pin are unsettled, the 3rd pin, 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin leads to Cross resistance Ry2 and connect the 13rd pin, connect the 13rd pin of operational amplifier U1 by resistance Rx2, connect by electric capacity Cy 9 pins, the 8th pin is directly connected to the 1st pin and the 3rd pin of multiplier U5, and the 13rd pin connects by resistance Ry 14 pins, the 14th pin connects the 9th pin by resistance R4；

1st pin of described operational amplifier U3 connects the 2nd pin by electric capacity Cz, connects the 6th pin by resistance R6, 1st pin is directly connected to the 3rd pin of multiplier U4, and the 3rd pin, the 5th pin, the 10th pin, the 12nd pin connect Ground, the 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin, the 9th pin are unsettled, and the 6th pin passes through resistance R7 connects the 7th pin, and the 7th pin connects the 13rd pin by resistance Rz2, and the 13rd pin connects the 14th by resistance Rz and draws Foot, the 14th pin connects the 2nd pin by resistance R5；

7th pin of the 1st pin concatenation operation amplifier U1 of described multiplier U4, the 2nd pin, the 4th pin, 6 pin ground connection, the 1st pin of the 3rd pin concatenation operation amplifier U3, the 5th pin meets VEE, and the 8th pin connects VCC, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance Ry3；

1st pin of described multiplier U5 and the 8th pin of the 3rd pin concatenation operation amplifier U2, the 2nd pin, 4 pins, the 6th pin ground connection, the 5th pin meets VEE, and the 8th pin meets VCC, and the 7th pin connects fortune by resistance Rz1 Calculate the 13rd pin of amplifier U3.

The construction method of the Lorenz type hyperchaotic system containing y side based on memristor the most according to claim 1, wherein magnetic Control is recalled and is led device and realized by operational amplifier U6 and multiplier U7 and multiplier U8, and described operational amplifier U6 concatenation operation is put Big device U1 and multiplier U7 and multiplier U8, multiplier U7 connect multiplier U8, multiplier U8 concatenation operation amplifier U2；

1st pin of described operational amplifier U6, the 2nd pin, the 3rd pin are unsettled, and the 4th pin meets VEE, and the 5th Pin ground connection, the 6th pin connects the 7th pin by electric capacity C4, draws by the 7th of resistance R8 concatenation operation amplifier U1 the Foot, the 7th pin is directly connected to the 1st pin and the 3rd pin of multiplier U7, and the 8th pin meets VCC；

1st pin of described multiplier U7 and the 7th pin of the 3rd pin concatenation operation amplifier U6, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin connects the 3rd pin of multiplier U8, the 8th pin Meet VCC；

1st pin of described multiplier U8 connects the 6th pin of operational amplifier U6 by resistance R8, by resistance R10 With series connection the 7th pin of resistance R9, the 1st pin is directly connected to the 7th pin of operational amplifier U1, the 2nd pin, 4th pin, the 6th pin ground connection, the 5th pin meets VEE, and the 7th pin meets the of operational amplifier U2 by resistance R9 13 pins, the 8th pin meets VCC.