Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations

Abstract

This paper proposes a single species system under seasonal succession and impulsive perturbations. The system is composed of two processes: one governed by the Gompertz equation, and the other modelled by the Logistic equation. The two processes are connected by impulse perturbations. Some very general, weak criteria on the permanence, existence, uniqueness and global stability of the positive periodic solution are established by analysis approaches based on the theory of discrete dynamical systems. The theoretical results are demonstrated by special examples and numerical simulations.