Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input

Taking both white noises and colored noises into account, a stochastic single-species model with Markov switching and impulsive toxicant input in a polluted environment is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Some simulation figures are introduced to illustrate the main results.

► Random population model with pulse toxicant input in polluted environments.
► Threshold between persistence and extinction is obtained.
► Different random noises have different effects on the persistence of the population.
► Impulsive period plays a key role in determining persistence of the population.
► Simulation figures support the analytical findings.