Threshold dynamics and pulse control of a stochastic ecosystem with switching parameters

This paper studies the stochastic dynamic behaviors and pulse control strategy for a vegetation ecosystem with switching parameters. First, a novel stochastic switching ecosystem is built by the variable perturbation, where the parameters are assumed to be time-varying functions. Then, based on the stochastic Ito^ formula and the theory of switched system, a sufficient condition of vegetation extinction in mean sense is established in detail, which provides a warning of the ecological degradation. Furthermore, in order to prevent ecological degradation, an achievable pulse control scheme is proposed, and the effectiveness of the pulse control is proved. Several numerical simulations are given to illustrate the developed threshold theorems and pulse control scheme.