Asymptotic stability of a periodic GA-predation system with infinite distributed lags on time scales

Abstract

The Gilpin-Ayala (GA) ecosystem is one of the most important biological mathematical models. The exploration of various kinetics behaviours of GA-ecological model has attracted the attention of many mathematicians. This paper focuses on a nonlinear periodic GA-predation ecosystem with infinite distributed lags on time scales. In the sense of time scale, our model unifies the difference model and differential model of GA-predation ecosystem. We first discuss a class of auxiliary functions with only two real roots. By using these auxiliary functions, coincidence degree and some inequality techniques, we next obtain some existence conditions of periodic solution. Furthermore, we explore the global asymptotic stability of periodic solution on account of Lyapunov stability theory. An example and its simulation are provided to inspect the correctness and availability of our main results at last.