Abstract

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Title:: Bifurcation analysis of memristor-coupled FHN-ML neuron model with time delay

Author(s):: ZHANG Meijiao; ZHANG Jiangang; WEI Lixiang; NAN Mengran; School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China

Keywords:: Keywords: FHN-ML neuron model Hopf bifurcation time delay firing pattern

Abstract:: Abstract: A model of memristor-coupled FHN-ML neurons with time delay is constructed to investigate the effects of different time delays on the dynamic behavior of the neuron system. The stability of the equilibrium point and the existence of the Hopf bifurcation in FHN-ML neuron system are proved by Routh-Hurwitz criterion and Hopf bifurcation theorem. The bifurcation direction and the stability of periodic solution of FHN-ML neural system are further proved by paradigm theory and center manifold theorem. The periodic bifurcation diagrams with reverse voltage and current frequency as two parameters and the inter-spike interval bifurcation diagrams with current frequency as single parameter are drawn by MATLAB software, and it is found that under the effect of time delay, the firing pattern of FHN-ML neuron system produces a delay phenomenon. With the increasing of time delay, the degree of delay increases, and the chaotic firing area decreases, and the number of periods with periodic bifurcation decreases. The results are helpful to understand the effect of delay effect on the firing activity of the coupled neural network under electromagnetic radiation exposures.