Fluctuation-enhanced stability of a metapopulation

The simplified incidence function model with cross-correlated noises was employed to study the stability of a metapopulation perturbed by environments. Through numerically computing the stationary probability distribution function (PDF) and stochastically simulating the extinction time of a metapopulation, we found that: (i) The multiplicative noise intensity D inhibits the fluctuation of dynamic variable while the additive noise intensity α intensifies it, whether there is a correlation between the multiplicative noise and the additive noise; (ii) As the correlation strength (λ) between them is greater than zero, there is an optimal D in which the PDF curve deviates furthest from the extinction position, and another optimal D which maximally delays the extinction time of a metapopulation; (iii) For the constant D and α, the increment of λ not only upgrades the probability that patches are occupied by a metapopulation, but also delays the time that a metapopulation goes to extinction.