Exploiting Invariant Manifolds of Memristor Circuits to Reproduce FitzHugh-Nagumo Dynamics

Abstract

A key feature of circuits with ideal memristors is that the state space is decomposed into infinitely many invariant manifolds where quite a rich dynamics can be displayed. In this paper the possibility of embedding known attractors into the circuit invariant manifolds is investigated. Specifically, we propose a simple RLC circuit, containing an ideal flux-controlled memristor, that is capable to replicate the dynamics of the FitzHugh-Nagumo model. It is shown that there is a one-to-one correspondence between the dynamic behaviors generated by the model for constant values of the injected current and those displayed onto the circuit invariant manifolds.