Structure analysis of the attracting sets for plankton models driven by bounded noises

In this paper, we study the attracting sets for two plankton models perturbed by bounded noises which are modeled by the Ornstein-Uhlenbeck process. Specifically, we prove the existence and uniqueness of the solutions for these random models, as well as the existence of the attracting sets for the random dynamical systems generated by the solutions. In order to further reveal the survival of plankton species in a fluctuating environment, we analyze the internal structure of the attracting sets and give sufficient conditions for the persistence and extinction of the plankton species. Some numerical simulations are shown to support our theoretical results.