Table of Contents
ISRN Biomathematics
Volume 2012 (2012), Article ID 546315, 7 pages
http://dx.doi.org/10.5402/2012/546315
Research Article

Transient Periodicity in a Morris-Lecar Neural System

1National Institute of Mental Health, NIH, Bethesda, MD 20892, USA
2Department of Mathematics, Faculty of Sciences, Jazan University, Jazan 45142, Saudi Arabia

Received 6 March 2012; Accepted 17 April 2012

Academic Editors: G. Bocharov, K. Kitano, J. R. C. Piqueira, and M. Santillán

Copyright © 2012 Sreenivasan Rajamoni Nadar and Vikas Rai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamical complexity of a system of ordinary differential equations (ODEs) modeling the dynamics of a neuron that interacts with other neurons through on-off excitatory and inhibitory synapses in a neural system was investigated in detail. The model used Morris-Lecar (ML) equations with an additional autonomous variable representing the input from interaction of excitatory neuronal cells with local interneurons. Numerical simulations yielded a rich repertoire of dynamical behavior associated with this three-dimensional system, which included periodic, chaotic oscillation and rare bursts of episodic periodicity called the transient periodicity.