Switching bifurcation of a Rulkov neuron system with ReLu-type memristor

In this paper, the flow switching theory is utilized to discuss the complex switching dynamics of a nonautonomous Rulkov neuron system with a ReLU-type memristor, and the conditions under which crossing and grazing motions of the Rulkov neuron system occur at the boundary are analyzed. Multistability of nonlinear system at the separation boundaries is revealed by the coexisting bifurcation diagrams, coexisting phase planes, and dual-parameter maps. A set of attractors in the case of the coexisting periodic and chaotic motions are studied by means of the simulation results of the trajectory mapping. Furthermore, field programmable gate array is utilized to design the Rulkov neuron system hardware experiments, and the experimental outcomes of the hardware implementations validate the numerical results.