Memristor Synapse-Based Morris–Lecar Model: Bifurcation Analyses and FPGA-Based Validations for Periodic and Chaotic Bursting/Spiking Firings

Abstract

Electromagnetic induction current sensed by the membrane potential in biological neurons can be characterized with a memristor synapse, which can be employed to demonstrate the real oscillating voltage patterns of Barnacle muscle fibers. This paper presents a 3D autonomous memristor synapse-based Morris–Lecar (abbreviated as m-ML) model, which is implemented through introducing a memristor synapse-based induction current to substitute the externally applied current in an existing 2D nonautonomous Morris–Lecar model. Making use of one- and two-parameter bifurcation plots and time-domain representations, diverse period-adding bifurcations as well as abundant periodic and chaotic burst firings are demonstrated. Through constructing the fold and Hopf bifurcation sets of fast spiking subsystem, bifurcation analyses of these chaotic and periodic burst firings are carried out. Moreover, the periodic and chaotic spiking firings and coexisting firing behaviors are illustrated by using one- and two-parameter bifurcation plots and local attraction basins. Finally, based on a field programmable gate array (FPGA) board, a compact digital electronic neuron is fabricated for the 3D m-ML model, from which periodic and chaotic bursting/spiking firings are experimentally measured to verify the results of the numerical simulations.