Impact of correlated Gaussian colored noises on stability and stationary probability density for the randomly forced two-species competitive Gompertz model. (April 2023) - Ma, Yuanlin; Yu, Xingwang
Abstract: In this paper, random factors described by correlated Gaussian colored noises are introduced into a two-species competition model with Gompertz growth. Firstly, stochastic stability is studied with the help of singular boundary theory. After that, the stationary probability density of the limiting system is given explicitly and then the extrema of invariant measure are discussed in detail. Finally, the average time of system escaping from the attraction domain is calculated using mean first passage time, and noise enhanced stability is observed. Our results show that random factors are more likely to make the system lose its original stability. Instead, the sample trajectories will stay near the maximum of the stationary probability density for a long time. Importantly, noise intensity and correlation degree are destructive, which can expand the distribution range of population density, weaken the stability of the system, and then easily lead to ecological imbalance. Conversely, the role of correlation time and proper competition between species is constructive and conducive to coexistence. Highlights: A two-species competition Gompertz model driven by correlated colored noises is proposed. The stability, the stationary probability density and the mean first passage time are discussed. Noise intensity and correlation degree are destructive, easily leading to ecological imbalance. Correlation time and proper competition between species are favorable for coexistence.