Spike Solutions for a Singularly Perturbed Differential Equation Modeling an Electrical Circuites: Flow Patterns and Bifurcations

Dr. Wenzhang Huang

Mathematical Sciences
University of Alabama in Huntsville

April 2, 2004
202 Madison Hall
3:00 PM (Coffee and Cookies at 2:30)

Abstract

We consider a singularly perturbed system of differential equations with periodic forcing which is derived from an electrical circuit model. The system presents the spiking phenomena over a one time period that has important application in signal processing and in the technology in communication. In this research we are particularly interested in the number of cycles a solution completes in one time period (which produces precisely the same number of spikes that can be used to transform the digital information) and the stability of spike's solutions. Sophisticated mathematical analysis has been developed that enable us to give a complete identification of subregions V_n, n = 1,2,... in the parameter space such that in each V_n the system produce stable spike's solutions with exactly n spikes.