Extinction Time of a Metapopulation Driven by Colored Correlated Noises

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 denotesthe extinction time (T_ex) 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 correlationstrength λ and its correlation time τ₃ play opposite roles on the T_ex; (ii) For the case of 0<λ<1, α and its correlation time τ₂ play opposite roles on theT_ex in which R>1 is the best condition, and there is one-peak structure on the T_ex-D plot; (iii) For the case of -1<λ ≤ 0, D and its correlation time τ₁ playopposite roles on the T_ex in which R<1 is the best condition and there is one-peak structure on the T_ex -τ₂ plot.