DYNAMICS OF ALMOST PERIODIC NICHOLSON’S BLOWFLIES MODEL WITH NONLINEAR DENSITY-DEPENDENT MORTALITY TERM

Abstract

This paper deals with the dynamics of almost periodic Nicholson’s blowflies model with nonlinear density-dependent mortality.  Prior to the main results, we prove the bounded-ness and extinction of the solutions for the addressed model.  By applying Shauder’s fixed point theorem, we establish sufficient conditions for the existence of almost periodic positive solution.  Under less restrictive assumptions, the exponential stability is derived by means of the Liapunov functional method.  The reported results give an affirmative answer to the problem raised by L. Berezansky.