Effects of colored noises on the statistical properties of a population growth model with Allee effect**Research is supported by the National Natural Science Foundation of China (11801224), Natural Science Foundation of Jiangsu Province (BK20180856).

Abstract

We study a stochastic population growth model with Allee effect, it is driven by correlated multiplicative and additive colored noises. The influences of noises on the statistical properties of the stochastic model are discussed. Applying an approximative Fokker-Planck equation, we first obtain the stationary probability distribution (SPD) of the stochastic model, and then present a more detailed discussion of how the noises determine the behaviors of the SPD, mean, variance and skewness of the population size. The research of the shape of SPD shows that the phenomenological bifurcation may occur when the noise intensity passes through a critical value. We also find that the additive and multiplicative noises have different effects on the moments (mean, variance and skewness) of population density.