Synchronization of Memristive Rulkov Neural Networks

doi:10.19596/j.cnki.1001-246x.8567

Abstract

Abstract:

We investigate collective dynamics of memristor Rulkov neural networks depend on electrical synapses and chemical synapses. It is found that for two memristive Rulkov neurons, the system can be synchronized regardless of coupling mode. At different coupling strengths, the neurons present different firing patterns, such as square wave, triangular wave, pulse firing, etc. As electrical synapses and chemical synapses coexist, synchronization of the system is more dependent on the strength of electrical coupling. Synchronization of globally coupled memristive Rulkov neural networks is studied. It is shown that as chemical synapses act alone, synchronization occurs within a certain region of coupling parameters. The synchronization is disrupted as the chemical coupling strength exceeds a certain threshold. As electrical synapses act alone, the system can reach a synchronized state quickly. It is also found that electrical coupling strength is the key factor to determine whether neurons are at rest or firing. As electrical coupling strength increases, firing frequency and amplitude of neuron increase. As electrical and chemical couplings coexist, the increase of coupling strength makes the neurons turn into arc discharge and reach synchronization. It provides a possible way to control firing patterns and synchronization of neural networks by adjusting coupling pattern and coupling strength.

Key words: neural network, memristor, electrical synapse, chemical synapse, synchronized firing

Lijun LIU, Duqu WEI. Synchronization of Memristive Rulkov Neural Networks[J]. Chinese Journal of Computational Physics, 2023, 40(3): 389-400.

Figures/Tables 16

Fig.1 Pinched hysteresis loops of the discrete memristor model (a) ω=0.01, (b) A=5

Fig.2 Bifurcation of neuron (a) original Rulkov model, (b) memristive Rulkov model (R1=0.8, R2=0.001, k=1, q0=0.1)

Fig.3 Waveforms of two memristive Rulkov neurons at (a) gc=0.1, (b) gc=0.29, (c) gc=0.31, (d) gc=0.38

Fig.4 Synchronization error of two memristive Rulkov neurons coupled via chemical synapses

Fig.5 Waveforms of two memristive Rulkov neurons at (a) ge= 0.15, (b) ge=0.35, (c) ge=0.5, (d) ge=1

Fig.6 Synchronization error of two memristive Rulkov neurons coupled via electrical synapses

Fig.7 Synchronization error of two memristive Rulkov models coupled via both electrical and chemical synapses

Fig.8 Waveforms of neurons (i = 10, 30, 50, 70, 90) at different gc with ge= 0.001

Fig.9 Developed spatial patterns of network at different gc with ge= 0.001 (a) gc= 0.001, (b) gc = 0.16, (c) gc = 0.3, (d) gc = 0.4

Fig.10 Synchronization error of memristive Rulkov models for global coupling of chemical synapses with gc=0.001

Fig.11 Waveforms of neurons (i = 10, 30, 50, 70, 90) at different ge with gc= 0.001

Fig.12 Developed spatial patterns of network at different ge with gc= 0.001 (a) ge= 0.08, (b) ge= 0.15, (c) ge=0.3, (d) ge= 0.7

Fig.13 Synchronization error of memristive Rulkov models for global coupling of chemical synapses with ge= 0.001

Fig.14 The waveforms of neurons (i = 10, 30, 50, 70, 90) for different ge and gc (a) ge= 0.02、gc= 0.01, (b) ge= 0.1、gc= 0.075, (c) ge= 0.12、gc= 0.062, (d) ge= 0.15、gc= 0.05

Fig.15 Developed spatial patterns of network for different ge and gc (a) ge= 0.02、gc= 0.01, (b) ge= 0.1、gc= 0.075, (c) ge= 0.12、gc= 0.062, (d) ge= 0.15、gc= 0.05

Fig.16 Synchronization error of globally coupled memristive Rulkov models co-existing electrical and chemical synapses

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