Noise-induced decline and propagation of population in the delayed Malthus–Verhulst model

Abstract

The effects of multiplicative and additive colored noises on decline and propagation processes of population in the delayed stochastic Malthus–Verhulst model are investigated by numerically computing and stochastically simulating. From the biological point of view, our results indicate that: the increasing correlation time of multiplicative noise strengthens the stability of population, and the correlation time of additive noise does not affect it. The increasing correlation time of multiplicative noise slows down the replacement of old individuals with young ones, while the increasing correlation time of additive noise with short delay time and the optimal correlation time of additive noise with long delay time quicken it.