<title>Periodicity, chaos, and the effects of noise in a forced Hodgkin-Huxley system</title>

Abstract

Nonlinear dynamical systems with feedback (dynamic) noise exhibit solutions which visit a large number of individual trajectories. Such systems will occasionally visit trajectories which converge to stable fixed points (or limit cycles), and will remain in these stable regimes until ejected by noise. Such systems exhibit ensemble behavior which is quite different from that of the noise-free case. We examine the effects of feedback noise in the Hodgkin-Huxley system for both constant and sinusoidally modulated applied current. We demonstrate that increasing noise levels causes the system to occasionally visit an otherwise rarely visited stable region of the manifold. Further increasing the noise level eventually obscures this behavior. We explore the potential for generating chaotic behavior via dynamic noise in this system under nominally periodic conditions. Ramifications for the analysis of systems undergoing transitions to chaos are discussed.