Periodic solutions of a logistic type population model with harvesting

Ping Liu
Junping Shi, William & Mary
Yuwen Wang
Junping Shi, William & Mary

Abstract

We consider a bifurcation problem arising from population biology du(t)/dl = f(u(t)) - epsilon h(t), where f(u) is a logistic type growth rate function, epsilon >= 0, h(t) is a continuous function of period T such that integral(T)(0) h(t)dt > 0. We prove that there exists an epsilon(0) > 0 such that the equation has exactly two T-periodic solutions when 0 < epsilon < epsilon(0), exactly one T-periodic solution when epsilon = epsilon(0), and no T-periodic solution when epsilon > epsilon(0). (C) 2010 Elsevier Inc. All rights reserved.