Dynamical Analysis and Circuit Implementation of a Memristor Synapse-coupled Ring Hopfield Neural Network

doi:10.19596/j.cnki.1001-246x.8338

Abstract

Abstract:

A new memristor model is proposed and three memristive characteristics are analyzed with standard nonlinear theory.Analog circuit of the memristor is designed.Then, a memristor synapse-coupled ring Hopfield neural network is constructed based on the memristor synapse.Special dynamical behaviors closely related to the memristor synapse are revealed by adopting bifurcation diagrams, Lyapunov exponents, time series, etc.It shows that the memristive neural network generates multiple symmetrical bursting firing patterns and complex chaotic behavior at different memristive synaptic weight.Finally, an equivalent analog circuit of the memristive neural network is designed, and correctness of MATLAB numerical simulation is verified with PSIM circuit simulations.

Key words: memristor, Hopfield neural network, bursting firing, coexisting attractors, analog circuit

Jia LUO, Liang SUN, Yinhu QIAO. Dynamical Analysis and Circuit Implementation of a Memristor Synapse-coupled Ring Hopfield Neural Network[J]. Chinese Journal of Computational Physics, 2022, 39(1): 109-117.

Figures/Tables 12

Fig.1 v-i curves at different input signal amplitude/frequency (a) pinched hysteresis loops at different amplitudes (F=0.2); (b) pinched hysteresis loops at different frequencies (A=2)

Fig.2 Circuit of a general memristor

Fig.3 PSIM simulation results of a locally active memristor circuit (a) pinched hysteresis loops at different voltage amplitudes (f=2 kHz); (b) pinched hysteresis loops at different voltage frequencies (H=2 V)

Fig.4 The structure of a memristor synapse-coupled loop neural network

Fig.5 Dynamical states related to memristor parameter α (a) bifurcation diagram; (b) Lyapunov exponents

Fig.6 Time sequences and phase plots in dynamical system under different memristive synaptic weight parameter α (a) periodic bursting firing (α=1); (b) chaotic bursting firing (α=10); (c) chaos firing (α=18); (d) period attractor (α=1); (e) chaos attractor (α=10); (f) chaos attractor (α=18); (g) periodic bursting firing (α=30); (h) periodic bursting firing (α=40); (i) periodic spiking firing (α=48); (j) period attractor (α=30); (k) period attractor (α=40); (l) period attractor (α=48)

Fig.7 Coexisting bursting behaviors under different initial conditions (a) symmetrical periodic bursting firing (α=1); (b) symmetrical chaotic bursting firing (α=10); (c) symmetrical periodic spiking firing (α=48)

Fig.8 Dynamical states related to memristive synaptic weight parameter β (a) bifurcation diagram; (b) Lyapunov exponents

Fig.9 Phase plots of attractor in system with different memristive synaptic weight parameter β (a) chaos attractor (β=0.3); (b) symmetrical quasi-period attractor (β=0.5); (c) symmetrical period attractor (β=0.6)

Fig.10 Circuit of memristor synapse-coupled loop Hopfield neural network

Fig.11 Simulation results of memristor synapse-coupled loop Hopfield neural network circuit (a) periodic bursting firng with RL1=50 kΩ (α=1); (b) symmetrical chaotic bursting firing with RL1=5 kΩ (α=10); (c) chaos firing with RL1=2.8 kΩ (α=18); (d) symmetrical periodic bursting firing with RL1=1.25 kΩ (α=40)

Fig.12 Simulation results of memristor synapse-coupled loop Hopfield neural network circuit (a) chaos attractor with RL2=166.67 kΩ (β=0.3); (b) symmetrical quasi-period attractor with RL2=100 kΩ (β=0.5); (c) symmetrical period attractor with RL2=83.33 kΩ (β=0.6)

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