Psychological effect on single-species population models in a polluted environment

We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results.