Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System

doi:10.19596/j.cnki.1001-246x.8649

Abstract

Abstract:

Memristor plays an important role in modeling nonlinear circuits and systems. Based on the proposed smooth quadratic generic memristor, this paper proposes a memristor-based Lorenz chaotic system. Different from the chaotic system on account of memristor feedback, this system takes a variable of the original Lorenz chaotic system as an inner state variable of memristor, so as to ensure that the system dimension does not increase. Stability analysis shows that the system has the same equilibrium point and stability as the original Lorenz system, namely, one unstable saddle point and two unstable saddle foci. By means of bifurcation diagram, Lyapunov exponent spectra, and phase plot, the dynamics of the proposed memristive system are revealed. The simulated results show that the memristive Lorenz chaotic system possesses coexisting bistable mode and self-similar bifurcation structures. What is more interesting is that the amplitude of the system can be regulated by changing the inner parameters of the generic memristor. Finally, the equivalent circuits of memristor and memristive system are designed and also synthesized by analog components. Simulation results confirm the correctness of the numerical simulations.

Key words: generic memristor, chaotic dynamics, Lorenz chaotic system, bistable mode, circuit implementation

CLC Number:

O415.5

Shuang ZHAO, Xiangjun CHEN, Yunzhen ZHANG. Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System[J]. Chinese Journal of Computational Physics, 2024, 41(2): 268-276.

Figures/Tables 8

Fig.1 Pinched hysteresis loops of the generic memristor at (a) input voltage A=2 with frequency f=0.1, 0.5, and 1; (b) input frequency f=0.5 with voltage A=1.7, 2, and 2.3

Fig.2 Phase plots of the memristive Lorenz chaotic system (a) x-y-z phase space; (b) x-y phase plane; (c) x-z phase plane; (d) y-z phase plane

Fig.3 Bifurcation behaviors with the change of parameter σ (a) bifurcation diagram; (b) Lyapunov exponent spectra

Fig.4 Two kinds of special bifurcation behaviors (a) coexisting bifurcation with the change of σ; (b) bifurcation behaviors with the change of parameter b

Fig.5 Coexisting attractor behaviors (a) σ = 2; (b) σ = 2.3; (c) σ = 2.44; (d) σ = 2.6

Fig.6 Butterfly attractors with (a) σ = 2.7 and g = 1; (b) σ = 2.7 and different values of g

Fig.7 (a) Equivalent circuit of generic memristor and its pinched hysteresis loops: (b) input voltage A = 2 with frequency F = 1 kHz, 5 kHz, and 10 kHz; (c) input frequency F = 5 kHz with voltage A = 1.7 V, 2 V and 2.3 V

Fig.8 (a) System equivalent circuit diagram and phase diagram verification: (b) x-y phase plane verification; (c) x-z phase plane verification; (d) y-z phase plane verification; (e) amplitude control verification

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