Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI

Abstract

Heterogeneous coexistence of multiple attractors was exhibited by a two-dimensional (2-D) non-autonomous model of adaptive synapse neuron with external excitation. Considering that electromagnetic induction (EMI) is an unavoidable interference in the electrophysiological environment, and memristors are often used to simulate the EMI induced by neuron membrane potentials, can the memristive EMI current be used instead of the external excitation current in the 2-D non-autonomous adaptive synapse neuron model? To this end, this paper proposes a three-dimensional (3-D) autonomous model of memristor-based adaptive synapse neuron (MASN) considering EMI. The MASN model has extremely many equilibrium points with complicated stability evolutions, resulting in the heterogeneous coexistence of extremely many attractors. The heterogeneously coexisting behaviors of the MASN model are investigated through some numerical methods, and the globally coexisting bifurcation behaviors, initials-relied kinetic distributions, and initials-sensitive riddled basins of attraction are thereby demonstrated. Furthermore, based on field programmable gate array (FPGA) platform, the MASN model is digitally implemented and the correctness of the numerical results is verified by hardware experiments.