Global asymptotic stability for a classical controlled nonlinear periodic AG-competitive ecosystem with distributed lags on time scales

Abstract

The Ayala-Gilpin (AG) kinetics system is an ecosystem mathematical model as famous as Lotka-Volterra kinetics system. This ecosystem model has been widely concerned and studied since it was proposed. This paper stresses on a classical controlled nonlinear periodic Ayala-Gilpin competitive ecosystem with distributed lags on time scales. In the sense of time scale, our model unifies and generalizes the discrete and continuous cases. Firstly, it is proved that a class of auxiliary functions have only two zeros in the real number field. Then, with the aid of the auxiliary function, using the coincidence degree theory and inequality technique, we obtain some sufficient criteria for the existence of periodic solutions of the model on a time scale. Meanwhile, we prove that the periodic solution is globally asymptotically stable by employing Lyapunov stability theory. Finally, an example is numerically simulated with the help of MATLAB tools.