Dynamics and Implementation of Memristive System Exhibiting Extreme Multistability

doi:10.19596/j.cnki.1001-246x.8760

Abstract

Abstract:

Based on a class of parameter-adjustable chaotic systems, an improved four-dimensional memristive chaotic system is established by replacing the gain resistor of the original system circuit with a memristor. Theoretical analysis demonstrates that the new system possesses two line equilibrium points and can generate self-excited attractors. The dynamics of the new system are analyzed through numerical simulation such as bifurcation diagrams, Lyapunov exponents, phase diagrams, etc. With the variation of initial conditions, the memristive system with fixed parameters exhibits not only the extreme multistability phenomenon of coexisting infinitely many attractors but also complex transient behaviors. Finally, to validate the theoretical and numerical simulation results, an equivalent circuit of the memristive chaotic system is designed, and hardware circuit experiments as well as PSIM circuit simulations confirm the correctness of the MATLAB numerical simulations.

Key words: flux-controlled memristor, line equilibrium, extreme multistability, transient behavior

CLC Number:

TN711.4

Ji CHEN, Yi XU, Jinfu LIU, Tao LIU. Dynamics and Implementation of Memristive System Exhibiting Extreme Multistability[J]. Chinese Journal of Computational Physics, 2024, 41(4): 523-534.

Figures/Tables 17

Fig.1 Circuit construction of memristor chaotic system

Fig.2 Equivalent circuit of system (1) and realization circuit of memristor chaotic system

Fig.3 Equivalent circuit of memristor

Fig.4 Phase portrait of typical attractor (a) x-z plane; (b) w-y plane

Fig.5 Dynamics of system (5) with respect to z(0) (a) bifurcation diagram; (b) Lyapunov exponents spectra

Fig.6 Dynamics of system (5) with respect to x(0) (a) bifurcation diagram; (b) Lyapunov exponents spectra

Fig.7 Dynamics of system (5) with respect to w(0) (a) bifurcation diagram; (b) Lyapunov exponents spectra

Fig.8 Dynamics of system (5) with respect to y(0) (a) bifurcation diagram; (b) Lyapunov exponents spectra; (c) mean values graph; (d)phase diagram of weak chaotic attractor

Fig.9 Phase portraits of the x-z plane with different initial conditions by MATLAB simulations (a) symmetrical single-wing chaotic attractor and symmetrical period-1 limitcycle; (b) symmetrical single-wing chaotic attractor and symmetrical period-2 limitcycle; (c) symmetrical single-wing chaotic attractor and symmetrical period-2 limitcycle; (d) four kinds of period-2 limitcycle; (e) two-wing chaotic attractor and four kinds of period-2 limitcycle

Table 1 Comparison of system (5) and some same type systems

系统	原系统编号	固定参数下共存吸引子数量
系统1^[31]	VB5	2
系统2^[32]	VB18	17
系统3^[33]	VB3	6
系统(5)	VB5	21

Fig.10 Time-domain waveform and phase portraits by MATLAB simulations with x(0) = 10-6, y(0) = w(0) = 0 at (a) z(0) = 0.28 and (b) z(0) = -0.29

Fig.11 Time-domain waveform and phase portraits by MATLAB simulations with x(0) = 10-6, y(0) = z(0) = 0, w(0) = -12.45

Table 2 Circuit parameter values of system(5)

参数	定义	数值	参数	定义	数值
R	电阻	36 kΩ	v_b	电压	1 V
C	电容	100 nF	R_w	电阻	36 kΩ
R_a	电阻	10 kΩ	R₁	电阻	3 kΩ
R_α	电阻	36 kΩ	R₂	电阻	10 kΩ
R_β	电阻	72 kΩ

Fig.12 Hardware circuit experiment (a) (vx-vz) plane phase portrait; (b) (vw-vy) plane phase portrait

Fig.13 Phase portraits in the (vx-vz) plane with different initial conditions by PSIM simulations (a)symmetrical single-wing chaotic attractor and symmetrical period-1 limitcycle; (b)symmetrical single-wing chaotic attractor and symmetrical period-2 limitcycle; (c)symmetrical single-wing chaotic attractor and symmetrical period-2 limitcycle; (d)four kinds of period-2 limitcycle; (e)two-wing chaotic attractor and four kinds of period-2 limitcycle

Fig.14 Time-domain waveform and phase portraits by PSIM simulations with vx(0) = 10-6 V, vy(0) = vw(0) = 0 V (a) vz(0) = 0.28 V; (b) vz (0) = -0.29 V

Fig.15 Time-domain waveform and phase portraits by PSIM simulations with vx(0) = 10-6 V, vy (0) = vz(0) = 0 V, vw(0) = -12.45 V

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