​Long-Term Dynamic Analysis of Endangered Species with Stage-Structure and Migrations in Polluted Environments

Abstract

We propose a stochastic stage-structured single-species model with migrations and hunting within a polluted environment, where the species is separated into two groups: the immature and the mature, which migrates from one patch to another with different migration rates. By constructing a Lyapunov function, together with stochastic analysis approach, the stochastic single-species model admits a unique global positive solution. We then utilize the comparison theorem of stochastic differential equations to investigate the extinction and persistence of solution to stochastic single-species model. The main results indicate that the species densities all depend on the intensities of random perturbations within both patches. As a consequence, we further provide several strategies for protecting endangered species within protected and unprotected patches.