Abstract: The environmental pollution problem caused by the rapid development of modern industry and agriculture and other production activities has become one of the most important ecological problems. In this paper, a new generalized single-species population model in polluted environment is established to study the influence of environmental toxins and food chain toxins on the existence of the specie. By using the average integral method, sufficient conditions for uniform persistence, non-persistent in the mean, weak persistence in the mean and extinction, and the threshold between weak persistence and extinction of the population are obtained. These results provide reliable scientific basis for the conservation of species and the management of the environment.

Key words: generalized Logistic model, polluted environment, population, persistence, extinction