CN104202144A - Rikitake system based balance-point-free four-dimensional hyper-chaos system and analog circuit - Google Patents

Rikitake system based balance-point-free four-dimensional hyper-chaos system and analog circuit Download PDF

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CN104202144A
CN104202144A CN201410439736.9A CN201410439736A CN104202144A CN 104202144 A CN104202144 A CN 104202144A CN 201410439736 A CN201410439736 A CN 201410439736A CN 104202144 A CN104202144 A CN 104202144A
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pin
multiplier
resistance
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operational amplifier
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CN104202144B (en
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胡春华
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Tongling Power Supply Co of State Grid Anhui Electric Power Co Ltd
TongAn Power Supply Co of State Grid Anhui Electric Power Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals

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  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
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Abstract

The invention provides a three-dimensional Rikitake chaotic system based balance-point-free four-dimensional hyper-chaos system and an analog circuit. According to the Rikitake system based balance-point-free four-dimensional hyper-chaos system and analog circuit, an inverting adding device and an inverting integrator are formed by an operational amplifier U1, an operational amplifier U2, a resistor and a capacitor; multiplication is achieved through multiplying units U3, U4 and U5; constant input is achieved through a one-V power source; the operational amplifier U1 and the operational amplifier U2 are in LF347N types; the multiplying units U3, U4 and U5 are in AD633JN types; the operational amplifier U1 is connected with the operational amplifier U2, the multiplying units U3 and the multiplying units U4; the operational amplifier U2 is connected with the multiplying units U5, the direct current power source and the multiplying units U1; the multiplying units U3 is connected with the operational amplifier U1; the multiplying unit U4 is connected with the operational amplifier U1; the operational amplifier U5 is connected with the operational amplifier U2; the one-V direct current power source is connected to the operational amplifier U2; a balance-point-free four-dimensional hyper-chaos system which is provided based on the three-dimensional Rikitake chaotic system is achieved through the analog circuit; a new method and idea are provided for application of the chaotic system into the engineering field such as the communication field.

Description

Based on Rikitake system without the four-dimensional hyperchaotic system of balance point and analog circuit
Technical field
The present invention relates to a chaos system and analog circuit, particularly one based on three-dimensional Rikitake chaos system without the four-dimensional hyperchaotic system of balance point and analog circuit.
Background technology
At present, the hyperchaotic system that oneself has is generally on the basis of three-dimensional chaotic system with three balance points, increase one dimension, formation has the four-dimensional hyperchaotic system that has a balance point at least, four-dimensional hyperchaotic system without balance point is not also suggested, the present invention is on the basis of three-dimensional Rikitake chaos system, a four-dimensional hyperchaotic system without balance point has been proposed, and realize with analog circuit, for chaos system, be applied to the engineering fields such as communication a kind of new method and thinking are provided.
Summary of the invention
The technical problem to be solved in the present invention be to provide a kind of based on three-dimensional Rikitake chaos system without balance point hyperchaotic system and analog circuit, the present invention adopts following technological means to realize goal of the invention:
1, based on Rikitake system without the four-dimensional hyperchaotic system of balance point, it is characterized in that being, comprise the following steps:
(1) Rikitake three-dimensional chaotic system i is:
dx / dt = - μx + yz dy / dt = - μy + ( z - a ) x dz / dt = 1 - xy i μ = 2 , a = 5
(2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
dz / dt = - μx + yz dy / dt = - μy + ( z - a ) x + w dz / dt = 1 - xy dw / dt = - ky ii μ = 2 , b = 40 , k = 3
(3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3, U4 and U5 to realize multiplying, utilize 1V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3, U4 and U5 adopt AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5,1V DC power supply 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 power supply concatenation operation amplifier U2;
The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin of U1, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin of U1, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin of U1, join, by resistance R 4 and the 9th pin of U1, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin of U2, by resistance R 12, connects ground connection after 1V power supply;
The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC.
The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC.
2, the analog circuit without the four-dimensional hyperchaotic system of balance point based on three-dimensional chaotic system, is characterized in that being, operational amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC power supply, consists of;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5, DC power supply 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 power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347D, and described multiplier U3, U4 and U5 adopt AD633JN;
The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin, join, by resistance R 4 and the 9th pin, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin, by resistance R 12, connects ground connection after 1V power supply;
The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC;
The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC;
Useful fruit of the present invention is: on the basis of three-dimensional Rikitake chaos system, a four-dimensional hyperchaotic system without balance point has been proposed, and realize with analog circuit, for chaos system, be applied to the engineering fields such as communication a kind of new method and thinking are provided.
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 are the actual connection layout of circuit of the present invention.
Embodiment
Below in conjunction with accompanying drawing and preferred embodiment, the present invention is further described in detail, referring to Fig. 1-Fig. 3.
1, based on Rikitake system without the four-dimensional hyperchaotic system of balance point, it is characterized in that being, comprise the following steps:
(1) Rikitake three-dimensional chaos chaos system i is:
dx / dt = - μx + yz dy / dt = - μy + ( z - a ) x dz / dt = 1 - xy i μ = 2 , a = 5
(2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
dz / dt = - μx + yz dy / dt = - μy + ( z - a ) x + w dz / dt = 1 - xy dw / dt = - ky ii μ = 2 , b = 40 , k = 3
(3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3, U4 and U5 to realize multiplying, utilize 1V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3, U4 and U5 adopt AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5,1V DC power supply 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 power supply concatenation operation amplifier U2;
The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin of U1, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin of U1, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin of U1, join, by resistance R 4 and the 9th pin of U1, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin of U2, by resistance R 12, connects ground connection after 1V power supply;
The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC;
The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC.
2, the analog circuit without the four-dimensional hyperchaotic system of balance point based on Rikitake system, is characterized in that being, operational amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC power supply, consists of;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5, DC power supply 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 power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347D, and described multiplier U3, U4 and U5 adopt AD633JN;
The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin, join, by resistance R 4 and the 9th pin, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin, by resistance R 12, connects ground connection after 1V power supply;
The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC;
The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC.
Resistance R 1=R2=R3=R6=R7=R8=R9=R11=10k Ω in circuit, R4=R10=50k Ω, R5=R12=100k Ω, R13=33.33k Ω, C1=C2=C3=C4=10nF.
Certainly, above-mentioned explanation is not limitation of the present invention, and the present invention is also not limited only to above-mentioned giving an example, and the variation that those skilled in the art make in essential scope of the present invention, remodeling, interpolation or replacement, also belong to protection scope of the present invention.

Claims (2)

  1. Based on Rikitake system without the four-dimensional hyperchaotic system of balance point, it is characterized in that being, comprise the following steps:
    (1) Rikitake three-dimensional chaos chaos system i is:
    dx / dt = - μx + yz dy / dt = - μy + ( z - a ) x dz / dt = 1 - xy i μ = 2 , a = 5
    (2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
    dz / dt = - μx + yz dy / dt = - μy + ( z - a ) x + w dz / dt = 1 - xy dw / dt = - ky ii μ = 2 , b = 40 , k = 3
    (3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3, U4 and U5 to realize multiplying, utilize 1V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3, U4 and U5 adopt AD633JN;
    Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5,1V DC power supply 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 power supply concatenation operation amplifier U2;
    The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin of U1, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin of U1, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin of U1, join, by resistance R 4 and the 9th pin of U1, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
    The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin of U2, by resistance R 12, connects ground connection after 1V power supply;
    The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
    The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC;
    The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC.
  2. 2. the analog circuit without the four-dimensional hyperchaotic system of balance point based on Rikitake system, is characterized in that being, operational amplifier U1, U2 and multiplier U3, U4, U5 and 1V DC power supply, consists of;
    Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and U4, described operational amplifier U2 connects multiplier U5, DC power supply 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 power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347D, and described multiplier U3, U4 and U5 adopt AD633JN;
    The 1st pin of described operational amplifier U1 joins by resistance R 7 and the 2nd pin, by resistance R 8 and the 6th pin, join, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, by resistance R 10 and the 6th pin, join, by resistance R 13 and the 6th pin of U2, join, connect the 1st pin of multiplier U3, connect the 3rd pin of multiplier U5, the 8th pin output x, by capacitor C 1 and the 9th pin, join, connect the 1st pin of multiplier U4, connect the 1st pin of multiplier U5, by resistance R 9 and the 6th pin, join, by resistance R 4 and the 9th pin, join, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
    The 1st, 2,13,14 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, and the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, joins by resistance R 5 and the 2nd pin of U1, and the 8th pin meets output z, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, the 9th pin joins by capacitor C 3 and the 8th pin, by resistance R 12, connects ground connection after 1V power supply;
    The 1st pin of described multiplier U3 connects the 7th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 13rd pin by resistance R 1, and the 8th pin meets VCC;
    The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 2nd pin by resistance R 6, and the 8th pin meets VCC;
    The 1st pin of described multiplier U5 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 9th pin by resistance R 11, and the 8th pin meets VCC.
CN201410439736.9A 2014-08-30 2014-08-30 The analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system Active CN104202144B (en)

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CN201610016170.8A CN105553640B (en) 2014-08-30 2014-08-30 The building method without equalization point four-dimension hyperchaotic system based on Rikitake systems
CN201410439736.9A CN104202144B (en) 2014-08-30 2014-08-30 The analog circuit of the hyperchaotic system of the four-dimension without equilibrium point based on Rikitake system
PCT/CN2015/000264 WO2016029619A1 (en) 2014-08-30 2015-04-14 Rikitake system-based four-dimensional super-chaotic system having no equilibrium point, and analog circuit

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CN105262579A (en) * 2015-09-09 2016-01-20 王晓红 Adaptive synchronization method and circuit for Rikitake-system-based four-dimensional hyperchaotic system without equilibrium point
WO2016029619A1 (en) * 2014-08-30 2016-03-03 李敏 Rikitake system-based four-dimensional super-chaotic system having no equilibrium point, and analog circuit

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CN110110494B (en) * 2019-06-09 2023-04-18 山东科技大学 Equivalent analog circuit of resistor is recalled to two local active absolute value magnetic controls
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