A stochastic single-species population model with partial pollution tolerance in a polluted environment

Abstract

We propose a single-species population model with partial pollution tolerance in a polluted environment in this contribution, and introduce the random perturbation of the birth rate of single-species population into this model. The extinction occurs around the pollution-free equilibrium under some moderate conditions, and the stationary distribution with ergodicity is derived around the positive equilibrium. Numerical simulations demonstrate the efficiency of our main results.