The mean extinction time and stability for a metapopulation system driven by colored cross-correlated noises

Abstract

In this paper, the stability for a metapopulation system driven by colored cross-correlated noises is investigated based on the Levins model. The stationary probability distribution and the explicit expression of the mean extinction time are derived according to the Fokker-Planck equation. Numerical results show that in the case of colored correlation between two noises, the addictive noise and the multiplicative noise intensity weaken the stability of metapopulation, and the correlation strength enhances the stability of metapopulation. If the correlation strength between the two noises is negative, the mean extinction time is a decreasing function of intensities of the two noises, but a increasing function of correlation time; if the correlation strength between the two noises is positive, then the mean extinction time is a decreasing function of addictive noise intensity and correlation time, but a non-monotonic function of multiplicative noise intensity.