Dynamical Analysis and Circuit Implementation of a Memristive Hopfield Neural Network

doi:10.19596/j.cnki.1001-246x.8386

Abstract

Abstract:

An extremely multistable memristive Hopfield neural network (HNN) is proposed which includes only three neurons and one multistable memristor synapse. Dissipativity and stability of equilibrium points are theoretically analyzed, and influence of memristive synapse-coupled strengths on dynamics in the memristive neural network is analyzed with numerical methods such as bifurcation diagrams, Lyapunov exponents, and phase plots. As network parameters are fixed, dynamical behavior of extreme multistability related to initial states is revealed. Finally, analog equivalent circuit of the memristive HNN is designed, and MATLAB numerical simulation results are verified with PSIM circuit simulation.

Key words: memristor, neural network, multistable, chaos, nonlinear circuit

Lihong TANG, Zongmei HE, Yanli YAO. Dynamical Analysis and Circuit Implementation of a Memristive Hopfield Neural Network[J]. Chinese Journal of Computational Physics, 2022, 39(2): 244-252.

Figures/Tables 11

Fig.1 Network topology of a memristive Hopfield neural network

Fig.2 Bifurcation diagram related to memristive intensity k

Fig.3 Lyapunov exponents related to memristive intensity k

Fig.4 Attractors of the memristive Hopfield neural network (a) Coexisting period-1 attractors (k=0.7); (b) Coexisting double scroll attractors and periodic attractors (k=1); (c) Coexisting period-3 attractors and period-1 attractors (k=1.4); (d) Coexisting single scroll attractors and periodic attractors (k=1.65)

Fig.5 Transient chaotic behavior k =1.29 (a) Time sequences; (b) Phase plot

Fig.6 Coexisting chaotic and periodic attractors related to initial values z(0) (a) Coexisting chaotic attractors on x1-x2-z three-dimensional view; (b) Coexisting chaotic attractors on x1-z plan view; (c) Coexisting periodic attractors on x1-x2-z three-dimensional view; (d) Coexisting periodic attractors on x1-z plan view

Fig.7 Bifurcation diagram related to z(0)

Fig.8 Basic circuit unit (a) Hyperbolic tangent function circuit; (b) Multistable memristor circuit

Fig.9 Memristive Hopfield neural network circuit

Fig.10 Circuit simulation results related to memristive synapse-coupled strength k (a) Periodic attractor RL=14.5 kΩ; (b) Chaotic attractor RL=8.2 kΩ

Fig.11 Circuit simulation results related to initial state z(0) (a) Coexisting chaotic attractors; (b) Coexisting periodic attractors

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