Local exponential stability of several almost periodic positive solutions for a classical controlled GA-predation ecosystem possessed distributed delays

Abstract

This paper deals with a classical controlled nonlinear almost periodic Gilpin-Ayala (GA) predation ecosystem possessed distributed delays. The existence of only two zeros of a class of auxiliary functions is obtained in R. On this basis, the multiplicity of almost periodic positive solutions for this ecosystem is investigated by some inequality techniques and theory of nonlinear analysis. Based on Lyapunov stability theory, we prove that this ecosystem is locally exponentially stable. A numerical example and simulation examine the correctness of our primary outcomes.