Studies of Nonlinear Phenomena in Sensory Systems

Abstract

Neurons being modeled into conductance-based models is extant in the literature since Hodgkin and Huxley. These models often show a rich variety of behaviors as nonlinear dy- namical systems. The Hodgkin-Huxley model, being four-dimensional, is difficult to study. Hence several subsequent lower-dimensional models have been suggested. Our aim in this project is to study the dynamical behaviors in a system of two non-identical neurons coupled together. In this venture, we use two such lower-dimensional models called the Hindmarsh- Rose model and the Morris-Lecar model. These two kinds of neurons were coupled unidirec- tionally and bidirectionally, and the resulting dynamics were studied. Resulting time series of the action potentials in the coupled systems for various sets of parameters and various strengths of coupling have been reported in this study. In some of the cases, the responsible bursting mechanisms have also been reported. We have also briefly covered the relevant concepts, such as the conductance models that have been used, classification of neurons ac- cording to their neurocomputational properties, classification of burst mechanisms according to the bifurcations responsible for them etc.