CN107092746A - A kind of circuit design method of the isomery magnetic control memristor model based on Chua circuits - Google Patents
A kind of circuit design method of the isomery magnetic control memristor model based on Chua circuits Download PDFInfo
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Abstract
A kind of circuit design method of the isomery magnetic control memristor model based on Chua circuits, (1) builds two isomery magnetic control memristor models with smooth cubic non-linearity characteristic；(2) (1) isomery memristor Chua chaotic systems characteristics are analyzed, verify whether it has memristor substantive characteristics；(3) (1) two memristor model is combined, a five rank isomery magnetic control memristor circuit models are built on classical three ranks Chua circuits；(4) circuit simulation is carried out to (3) using Multisim softwares, and be compared with (2) numerical computations, the correctness and memristor reliability of the designed isomery magnetic control memristor model of checking.The present invention passes through numerical simulation and Circuit verification, memristor model is respectively provided with the VA characteristic curve of the tight hysteresis curve of class of the oblique figure of eight, chaotic behavior can be produced by demonstrating the double isomery memristor Chua circuits newly built simultaneously, with complicated nonlinear dynamic characteristic.
Description
Technical field
The invention belongs to the Systems Theory model in nonlinear kinetics and analog circuit field, be related to chaology,
Memristor and circuit design and the Realization of Simulation.
Background technology
The Cai Shaotang (Chua) of foreign citizen of Chinese origin scientist University of California Berkeley of the U.S. teach in 1971 according to voltage V with
Electric current i, magnetic fluxWith the relation between electric current i, quantity of electric charge q and voltage V, thus it is speculated that going out one can be for expression magnetic flux
The presence of the element of relation between quantity of electric charge q, referred to as memristor, the so far pass in Circuit theory between four basic circuit variables
System reaches complete finally.2008, the Stanley Williams in HP laboratories etc. existed《Nature》On reported a kind of new
The nanoscale solid state element with memristor characteristic, so as to further demonstrate Chua in the presence for the memristor predicted before 37 years
Property.It is that the design and application of circuit bring wider development space due to the special memory of memristor and nonlinear characteristic,
Realization including memristor circuit modeling, the grand modelings of SPICE, I-V Characteristic Analysis and its equivalent circuit etc..
Memristor is a nonlinear passive Two-port netwerk element, exists in nonlinear circuit and is widely applied.South Korea
Professor Kim proposes the memristor bridge circuit being made up of four identical memristor elements, can complete nerve cell cynapse computing and
Realize weighting and weights programming；Wang Lidan and Duan Shukai of Southwestern University etc. are constructed on the basis of HP TiO2 memristor models
One memristor chaos circuit, generates corresponding chaos attractor；Ahamed and Lakshmanan is ground to memristor MLC circuits
Study carefully, Germicidal efficacy has arrived the complicated phenomenons such as Non-smooth surface bifurcated, transient state hyperchaos and hyperchaos pulsation；Bag Bocheng of Changzhou University etc.
Using cubic non-linearity memristor model, the equivalent circuit of magnetic control memristor is realized, and the correlation properties of circuit are carried out
Experimental analysis.Song Dehua and Lv Mengfei of Beijing University of Post ＆ Telecommunication etc. are based on the HP TiO2 memristor nonlinear models for having border, to recalling
The series and parallel hindered with electric capacity, inductance is studied, and analyzes characteristic and driving frequency and electric capacity, inductance that circuit has
Influence of the parameter to circuit.
The content of the invention
The purpose of the present invention is to propose to a kind of circuit design method of the isomery magnetic control memristor model based on Chua circuits,
Two isomery magnetic control memristor models are built on the Chua circuits of standard, and electronic circuit is designed with universal electric element, together
When theoretical simulation and experimental analysis have been carried out to the dynamics of the model, verify isomery magnetic control memristor Chua chaos of electronic circuits rows
For diversity and realizability.
A kind of circuit design method of isomery magnetic control memristor model based on Chua circuits of the present invention, including with
Lower step：
(S01)：Build two isomery magnetic control memristor models with smooth cubic non-linearity characteristic；
Wherein：Respectively two memristor magnetic flux, q1,q2Respectively add up the electric charge by two memristors
Amount, a, b, c, d, e is parameter.
(S02)：(S01) isomery memristor Chua chaotic systems characteristics are analyzed, verify whether it has memristor substantive characteristics；
(S03)：With reference to (S01) two memristor models, a five rank isomery magnetic are built on classical three ranks Chua circuits
Control memristor circuit model.
(S04)：(S02) numerical computations and (S03) circuit simulation are compared, the designed isomery magnetic control memristor of checking
The correctness and memristor reliability of device model.
Further, Detailed operating procedures of the present invention are as follows：
Step 1：Build two isomery magnetic control memristor models with smooth cubic non-linearity characteristic.
1) structure magnetic control memristor 1, the Nonlinear Characteristic Curve with three times smooth monotone increasings, i.e.,：
Can obtain its magnetic control recall lead for：
2) magnetic control memristor 2, the equally Nonlinear Characteristic Curve with three times smooth monotone increasings are built：
Can obtain its magnetic control recall lead for：
Wherein：Respectively two magnetic control memristor magnetic flux, q1,q2Respectively add up by two magnetic control memristors
The quantity of electric charge of device, a, b, c, d, e is parameter.Select a=2, b=2, c=0.75, d=2, e=0.1, can obtain such as Fig. 1 and
Two magnetic control memristors of Fig. 2Characteristic curve andCharacteristic curve.
Step 2：The chaotic characteristic of isomery memristor Chua system models is analyzed, verifies whether it has the essence of memristor special
Levy.
In order to verify that magnetic control memristor has the tight hysteresis curve characteristic of class Jing Guo the oblique figure of eight of origin, the present invention is in magnetic
Control memristor two ends and apply a sinusoidal voltage v=sin (wt), if the electric current for flowing through magnetic control memristor is i, then can obtain magnetic
Energy：
Same selection a=2, b=2, c=0.75, d=2, e=0.1, Fig. 3 and Fig. 4 sets forth two magnetic control memristors
VA characteristic curve of the device under different angular frequency w, angular frequency is bigger, and it is compacter that the oblique figure of eight is shunk, and can be tested with this
The isomery model of the card present invention has memristor characteristic.
Step 3：Based on three classical rank Chua circuit theories, a five rank isomery magnetic control memristor circuit models are built；
1) three classical rank Chua chaos circuits are as shown in figure 5, wherein comprising two electric capacity C1And C2, an inductance L and
One Chua diodes NR(nonlinear resistance).
2) present invention is negative with the magnetic control memristor 1 of step 1 and one on the basis of three classical rank Chua chaos circuits
The active memristor circuit that conductance G is constituted inserts to replace the Chua diodes in primary circuit, then between LC resonance portion circuits
(Fig. 6) two memristors are symmetrical in the magnetic control memristor 2 of step 1, the novel circuit so formed, but the equation of structure is different.
3) it can be obtained by Kirchhoff's law and the C-V characteristic of element, the circuit state equation shown in Fig. 6 is one five
The first order differential equation system of simultaneous：
Wherein, v1, v2It is electric capacity C respectively1, C2The voltage at two ends, i3It is the electric current for flowing through inductance L and resistance r from top to bottom,WithRespectively formula (4) and the magnetic control of (6), which are recalled, leads value.
Step 4：Step 2 numerical computations and step 3 circuit simulation are compared, the designed isomery magnetic control memristor of checking
The correctness and memristor reliability of device model.
1) x=v is set1, y=v2, z=i3,
ξ=G, and define nonlinear function：
Then the state equation of (7) formula can be rewritten as：
Therefore, isomery magnetic control memristor Chua chaos circuits are one five and maintain system, and its nonlinear dynamical equation can be with
Described by formula (10).
2) x (v are shown in Fig. 7 (a), (b), (c) respectively1), y (v2), z (i3) chaos attractor track；Fig. 8 (a), (b)
Respectively it is shown that the magnetic flux of magnetic control memristor 1With voltage v1Between relation, and the magnetic flux of magnetic control memristor 2With
Voltage v2Between relation, they have a double scroll chaos；Two magnetic controls are shown in Fig. 9 (a), (b) respectively
Relation between memristor voltage and electric current, shows oblique " 8 " the hysteresis curve pattern similar with Fig. 4 with Fig. 3.
3) Figure 10 is isomery magnetic control memristor Chua circuit simulation overall structure figures of the present invention, and Figure 11 is using Multisim electricity
Each variable phasor of road emulation.Figure 11 Simulation results and the discovery of Fig. 7 numerical results, the isomery magnetic designed by the present invention
The correctness of memristor model is controlled, can be with physics realization in actual circuit.
The method have the characteristics that：The nonlinear diode pole of the memristor model that HP Lab uses and Chua circuits
To be similar, chaotic oscillator can be realized with reference to other circuit elements.The present invention is on the basis of classical three-dimensional Chua circuits
On, substitute the diode in Chua chaos circuits using magnetic control memristor, another magnetic control memristor position with its on
Electric capacity formation symmetrical structure, constructs an isomery magnetic control memristor Chua circuit.Entered using Matlab/Multisim two ways
Row numerical simulation and Circuit verification, the C-V characteristic that the movement locus of variable is respectively provided with the tight hysteresis curve of class of the oblique figure of eight are bent
Line, while chaotic behavior can be produced by demonstrating the double isomery memristor Chua circuits newly built, with complicated non-linear dynamic
Learn characteristic.
Brief description of the drawings
Fig. 1 is the magnetic control memristor 1 that the present invention is built and magnetic control memristor 2Characteristic curve.
Fig. 2 is the magnetic control memristor 1 that the present invention is built and magnetic control memristor 2Characteristic curve.
The hysteresis curve for the magnetic control memristor 1 that Fig. 3 builds for the present invention.
The hysteresis curve for the magnetic control memristor 2 that Fig. 4 builds for the present invention.
Fig. 5 is classical three-dimensional Chua chaos circuit figures.
The isomery magnetic control memristor Chua circuit models that Fig. 6 builds for the present invention.
Fig. 7 is chaos attractor trajectory diagram of the present invention.Wherein, (a) is x (v1)-y(v2) chaos attractor track, (b) is y
(v2)-z(i3) chaos attractor track, (c) is y (v2)-z(i3) chaos attractor track.
Fig. 8 is the relation between magnetic control memristor magnetic flux of the present invention and voltage, wherein, (a) is the magnetic flux of magnetic control memristor 1With voltage x (v1) between relation, (b) be the magnetic flux of magnetic control memristor 2With voltage x (v2) between relation.
Fig. 9 is the relation between the present invention two magnetic control memristor voltage v and electric current i, wherein, (a) is magnetic control memristor
1, (b) is magnetic control memristor 2.
Figure 10 is isomery magnetic control memristor Chua circuit simulation overall structure figures of the present invention.
Figure 11 is variable phasor of the present invention using Multisim circuit simulations, wherein, (a) is x-y plane phasor, (b)
For x-z-plane phasor, (c) is y-z plane phasor.
The equivalent circuit of magnetic control memristor 1 that Figure 12 builds for the present invention.
The memristor hysteresis curve result of magnetic control memristor 1 that Figure 13 builds for the present invention.
The equivalent circuit of magnetic control memristor 2 that Figure 14 builds for the present invention.
The memristor hysteresis curve result of magnetic control memristor 2 that Figure 15 builds for the present invention.
Embodiment
The present invention is described in further detail below with reference to accompanying drawing.
Embodiment 1：Isomery memristor Chua system values are analyzed.
To formula (10) Selecting All Parameters：α=10, β=16.67, γ=0.28, η=1, ξ=2.75, C1=0.2, C2=2,
R=0.5, L=0.06, r=0.0168, a=2, b=2, c=0.75, d=2, e=0.1, then equation (10) be changed into：
It is (0,0,10 for primary condition-10, 0.2,1.99), system (11) generates double scroll chaos, it
Projection and time domain waveform in phase plane are as shown in Figure 7, Figure 8 and Figure 9..
Embodiment 2：The circuit design of isomery magnetic control memristor 1.
The magnetic control memristor 1 constructed for step 1, its equivalent circuit diagram is as shown in figure 12.Wherein operational amplifier U1And U5
Constitute a voltage follower, operational amplifier U2And R1C1With operational amplifier U6And R3C2All constitute an integrator, computing
Amplifier U3It is accomplished that the effect of an adder, operational amplifier U4And R10,R11The circuit of composition causes R9Resistance become
Into negative, U7And R4,R5A reverser is constituted, the memristor hysteresis curve of magnetic control memristor 1 is as shown in figure 13.
Embodiment 3：The circuit design of isomery magnetic control memristor 2.
The magnetic control memristor 2 constructed for step 1, its equivalent circuit diagram is as shown in figure 14.Operational amplifier U1Constitute one
Individual voltage follower, can effectively prevent load effect.Operational amplifier U2And resistance R1With electric capacity C1Constitute an integration
Device, it is exported after two multipliers, realizes the nonlinear operation of magnetic control memristor.U3And R3,R4The circuit of composition
Effect be in order that R2Resistance become negative, the related operation after being easy to.The memristor hysteresis curve of magnetic control memristor 2 is as schemed
Shown in 15.
Embodiment 4：Isomery magnetic control memristor integrated circuit is realized.
In order to verify the feasibility and correctness of numerical computations, using Multisim simulation softwares step 1 is constructed it is different
Structure magnetic control memristor Chua circuits are emulated, and it emulates integrated circuit figure and is illustrated in fig. 10 shown below.The component parameter of each in circuit
Value is respectively set to：
R1=R2=R3=R5=R9=R10=R11=R12=R13=R18=R19=R26=R27=100k Ω,
R4=R6=R7=R8=R16=R17=R20=R21=R22=R23=R28=R29=10k Ω,
R14=95.24k Ω, R15=200k Ω, R24=6k Ω, R25=357.14k Ω, C1=C2=C3=C4=C5=
33nF。
Amplifier uses LF347 in Figure 10, and multiplier, electric capacity and resistance are basic first device in Multisim
Part.The temperature drift characteristic due to analog circuit and the shadow of electromagnetic radiation effect are can be seen that from Figure 11 and Fig. 7 oscillogram
Ring, be affected the accuracy of system, result in experimental result and numerical simulation has differences, but totally meet consistent
Property.
The present invention proposes that two have smooth cubic non-linearity characteristic and the tight hysteresis curve VA characteristic curve of oblique " 8 " word class
Isomery memristor, based on traditional three-dimensional Chua circuits, construct the equivalent-circuit model of two isomery magnetic control memristors, electricity
Road emulation is consistent with Numerical Simulation Results, shows that isomery magnetic control memristor Chua circuits have abundant chaos system characteristic and complexity
The diversity of dynamic behavior.
Claims (1)
1. a kind of circuit design method of the isomery magnetic control memristor model based on Chua circuits, it is characterized in that including following step
Suddenly：
(S01) two isomery magnetic control memristor models with smooth cubic non-linearity characteristic are built：
Wherein：Respectively two memristor magnetic flux, q1,q2The respectively accumulative quantity of electric charge for passing through two memristors, a,
B, c, d, e are parameter；
(S02) (S01) isomery memristor Chua chaotic systems characteristics are analyzed, verify whether it has memristor substantive characteristics；
(S03) (S01) two memristor models are combined, a five rank isomery magnetic control memristors are built on classical three ranks Chua circuits
Circuit model；
(S04) circuit simulation is carried out to (S03) using Multisim softwares, and be compared with (S02) numerical computations, verify institute
The correctness and memristor reliability of the isomery magnetic control memristor model of design.
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Cited By (10)
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| CN108090308A (en) * | 2018-01-18 | 2018-05-29 | 重庆邮电大学 | A kind of elementary cell chaos circuit based on HP memristors and capacitor |
| CN108418674A (en) * | 2018-04-19 | 2018-08-17 | 沈阳建筑大学 | A kind of five dimension chaos circuits containing series connection memristor |
| CN108491567A (en) * | 2018-02-05 | 2018-09-04 | 杭州电子科技大学 | A kind of Simulink modeling methods of flux-controlled memristor |
| CN108804786A (en) * | 2018-05-26 | 2018-11-13 | 江西理工大学 | A kind of memristor precircuit design method that associative neural network synaptic weight is plastic |
| CN109086558A (en) * | 2018-09-29 | 2018-12-25 | 杭州电子科技大学 | The local active memristor emulator of logarithmic |
| CN109359400A (en) * | 2018-10-25 | 2019-02-19 | 江西理工大学 | A kind of double magnetic control memristor Model Digitization circuit design methods of the isomery based on DSP Builder |
| CN110032830A (en) * | 2019-05-20 | 2019-07-19 | 成都师范学院 | Cubic non-linearity magnetic control memristor simulator based on current transmission device |
| CN112784432A (en) * | 2021-01-29 | 2021-05-11 | 南昌师范学院 | Dynamic characteristic analysis method of first-order RC equivalent circuit dynamic model of lithium ion battery |
| CN114528794A (en) * | 2022-02-14 | 2022-05-24 | 江西理工大学 | Fractional order chaotic circuit design method based on mixed memristor |
| CN116011536A (en) * | 2022-12-06 | 2023-04-25 | 常州大学 | Nerve morphology circuit based on local active memristor |
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| CN108090308B (en) * | 2018-01-18 | 2021-07-13 | 重庆邮电大学 | HP memristor and capacitor-based basic unit chaotic circuit |
| CN108090308A (en) * | 2018-01-18 | 2018-05-29 | 重庆邮电大学 | A kind of elementary cell chaos circuit based on HP memristors and capacitor |
| CN108491567A (en) * | 2018-02-05 | 2018-09-04 | 杭州电子科技大学 | A kind of Simulink modeling methods of flux-controlled memristor |
| CN108491567B (en) * | 2018-02-05 | 2021-09-07 | 杭州电子科技大学 | Simulink modeling method of magnetic flux control type memristor |
| CN108418674A (en) * | 2018-04-19 | 2018-08-17 | 沈阳建筑大学 | A kind of five dimension chaos circuits containing series connection memristor |
| CN108804786A (en) * | 2018-05-26 | 2018-11-13 | 江西理工大学 | A kind of memristor precircuit design method that associative neural network synaptic weight is plastic |
| CN108804786B (en) * | 2018-05-26 | 2022-04-15 | 江西理工大学 | Memristive model circuit design method for realizing plasticity of synaptic weights of associative neural network |
| CN109086558A (en) * | 2018-09-29 | 2018-12-25 | 杭州电子科技大学 | The local active memristor emulator of logarithmic |
| CN109359400A (en) * | 2018-10-25 | 2019-02-19 | 江西理工大学 | A kind of double magnetic control memristor Model Digitization circuit design methods of the isomery based on DSP Builder |
| CN109359400B (en) * | 2018-10-25 | 2023-08-15 | 江西理工大学 | Digital circuit design method of heterogeneous double-magnetic control memristor model based on DSP Builder |
| CN110032830A (en) * | 2019-05-20 | 2019-07-19 | 成都师范学院 | Cubic non-linearity magnetic control memristor simulator based on current transmission device |
| CN110032830B (en) * | 2019-05-20 | 2023-11-14 | 成都师范学院 | Three-time nonlinear magnetic control memristor simulator based on current transmitter |
| CN112784432A (en) * | 2021-01-29 | 2021-05-11 | 南昌师范学院 | Dynamic characteristic analysis method of first-order RC equivalent circuit dynamic model of lithium ion battery |
| CN112784432B (en) * | 2021-01-29 | 2023-04-18 | 南昌师范学院 | Dynamic characteristic analysis method of first-order RC equivalent circuit dynamic model of lithium ion battery |
| CN114528794A (en) * | 2022-02-14 | 2022-05-24 | 江西理工大学 | Fractional order chaotic circuit design method based on mixed memristor |
| CN114528794B (en) * | 2022-02-14 | 2024-05-07 | 江西理工大学 | Fractional order chaotic circuit design method based on hybrid memristor |
| CN116011536A (en) * | 2022-12-06 | 2023-04-25 | 常州大学 | Nerve morphology circuit based on local active memristor |
| CN116011536B (en) * | 2022-12-06 | 2024-01-23 | 常州大学 | Nerve morphology circuit based on local active memristor |
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