PERIODIC SOLUTIONS FOR AN EQUATION GOVERNING DYNAMICS OF A RENEWABLE RESOURCE SUBJECTED TO ADDITIVE ALLEE EFFECTS IN A SEASONALLY VARYING ENVIRONMENT

Abstract

In this article the minimum number of positive periodic solutions admitted by a non-autonomous scalar differential equation is estimated. This result is employed to find the minimum number of positive periodic solutions admitted by a model representing dynamics of a renewable resource that is subjected to additive Allee effects in a seasonally varying environment. Leggett-Williams multiple fixed point theorem is used to establish the existence of at least two positive periodic solutions for the considered dynamic equation. Two methods are obtained to establish the existence of periodic solutions. Key results are illustrated through numerical simulation.