Extinction Time of a Metapopulation Driven by Colored Correlated Noises

Abstract

The simplified incidence function model which is driven by the colored correlated noises is employed to investigate the extinction time of a metapopulation perturbed by environments. The approximate Fokker–Planck Equation and the mean first passage time which denotes the extinction time (Tex) are obtained by virtue of the Novikov theorem and the Fox approach. After introducing a noise intensity ratio and a dimensionless parameter R = D/α (D and α are the multiplicative and additive colored noise intensities respectively), and then performing numerical computations, the results indicate that: (i) The absolute value of correlation strength Λ and its correlation time τ3 play opposite roles on the Tex; (ii) For the case of 0 < Λ < 1, α. and its correlation time τ2 play opposite roles on the Tex in which R > 1 is the best condition, and there is one-peak structure on the Tex – D plot; (iii) For the case of −1 < A ≤ 0, D and its correlation time τ1 play opposite roles on the Tex in which R < 1 is the best condition and there is one-peak structure on the Tex – τ2 plot.