Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching

Abstract

In this paper, we stochastically perturb the harvesting mutualism system into stochastic system in a polluted environment by white noise, telegraph noise and Lévy jump. We first prove the existence and uniqueness of the global positive solution of the stochastic system, and establish the sufficient condition for persistence in mean of the two cooperative species. Then using aggregation and ergodic methods, the explicit forms of optimal harvesting strategy and the maximum of sustainable yield are obtained. We also give some examples and numerical simulations to illustrate the theoretical results. The impacts of toxicant in organism, telegraph noise and Lévy jump on the persistence in mean and optimal harvesting strategy are revealed.