Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model

The problem of analyzing the mechanisms of variability in neural dynamics caused by memristive connections is considered. This problem is studied on the base of a neuron model combining the Rulkov map and discrete memristor. The extreme multistability of this 3D model is explained by the existence of a continuum family of invariant 2D planes. We show transformations of the system dynamics caused by an increase of the strength of magnetic induction current. Memristor-induced multistage transitions between order and chaos, resulting in formation of chaotic bursts through Canard explosion, are studied.