Permanence and almost periodic solution of a discrete impulsive Richards growth equation with variable delays and feedback control

In the old years, the researchers usually considered the permanence and almost periodic dynamics of the discrete time models without impulsive perturbations in biological populations. In this paper, we study a discrete impulsive Richards growth equation with variable delays and feedback control. By using some analysis technics and constructing a suitable Lyapunov functional, we investigate the permanence and global attractivity of the model. Based on the results of permanence and global attractivity, some sufficient conditions for the existence of a unique globally attractive positive almost periodic solution to the model are established, by the relation between the solutions of impulsive system and the corresponding non-impulsive difference system, and the almost periodic functional hull theory of difference system. To some extent, our main results complement and generalize some scientific work in recent years. Finally, some examples and numerical simulations are given to illustrate the effectiveness of our main results.