Bifurcation, Chaos and Suppression of Chaos in FitzHugh-Nagumo Nerve Conduction Model Equation

Abstract

We study the effect of constant and periodic membrane currents in neuronal axons described by the FitzHugh-Nagumo equation in its wave form. Linear stability analysis is carried out in the absence of periodic membrane current. Occurrence of chaotic motion, (i) in the absence of both constant and periodic membrane currents, (ii) with constant current only, (iii) with periodic membrane current only, and (iv) with both constant and periodic currents is investigated for specific parametric choices. We show how chaos sets in through a cascade of period doubling bifurcations. We then demonstrate the possibility of control of chaos using various control mechanisms. Specifically, we show the control of chaos by (i) adaptive control mechanism, (ii) periodic parametric perturbation and (iii) stabilization of unstable periodic orbits.