Intermittent dispersal population model with almost period parameters and dispersal delays

Abstract

We establish a class of intermittent bidirectional dispersal population models with almost periodic parameters and dispersal delays between two patches. The form of dispersal discussed in this paper is different from both continuous and impulsive dispersals, in which the dispersal behavior occurs either in a sustained manner or instantaneously; instead, it is a synthesis of these types. Dynamical properties such as permanence, existence, uniqueness, and globally asymptotic stability of almost periodic solutions are investigated by using Liapunov-Razumikhin type technique, using the comparison theorem, constructing a suitable Lyapunov functional, using almost periodic functional hull theory and analysis approach, etc. Finally, numerical simulations are presented and discussed to illustrate our analytic results, by which we find that intermittent dispersal systems are more complicated than continuous or impulsive dispersal systems.