Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model

Abstract

The qualitative behavior of the differential equation , where x is real and f is periodic in t, is determined by the attracting periodic solutions. This article gives an exposition of a method of Ilyashenko that uses complex analysis to determine an upper bound on the number of periodic solutions. The method is then applied to a well-known model of a single neuron or pool of neurons.