Study on the onset bifurcations of a Morris-Lecar neuron under a periodic current

Abstract

Nervous systems under periodic stimuli display rich dynamical states, including mode-locking and chaotic responses, which have been the subject of intentive studies in neurodynamics. In this paper, the bifurcation structure of a Morris-Lecar neuron under a sinusoidal stimulus is investigated, focusing on the mechanisms of the firing onset with the help of bifurcation and continuation algorithms. This system exhibits a simple bifurcation structure with a bell-shaped firing onset without hysteresis. In particular, at high frequency periodic forcing, an interesting dynamical state with a bursting-like behavior appears This study provides useful insight into the firing onset of various neural systems under periodic forcing.