Effect of noises on the stability of a metapopulation

Abstract

The Levins model subjected to the noise is employed to study the stability of a metapopulation. The analytic expressions of the stationary probability distribution function and the mean extinction time of the metapopulation are obtained according to the Fokker-Planck Equation. The results show that for the case of no correlation between the additive noise and the multiplicative noise (=0, is the intensity of correlation between multiplicative and additive noise), the increase of the additive noise intensity weakens the stability of a metapopulation; for the case of 0, enhances the stability of a metapopulation. For -(c-e-D)2/(4cD)1, can induce the resonance restrain phenomenon. Meantime, there exists a critical value of D. When D is lower than the critical value, the stability of the system is enhanced.

Influence of Noise on Stability of the Ecosystem

“…[7−8] In a four-species ecological system with cyclic dominance, phase transition from the coexistence of all four species to the existence of only two neutral species emerges through the changing of parameter across the threshold value. [9] In addition, some research work focus on the noise [10] and time-delay. [11] Based on Levins model with only one species, Wang [10] et al find multiplicative and additive noise can influence the stability of the meta-population.…”

“…[9] In addition, some research work focus on the noise [10] and time-delay. [11] Based on Levins model with only one species, Wang [10] et al find multiplicative and additive noise can influence the stability of the meta-population. Based on the classical Lotka-Volterra model of one-species, the Stochas-tic Resonance (SR), which is a common phenomena in nonlinear noisy system, is theoretically and numerically observed.…”