噪声对集合种群稳定性的影响

本文在Levins模型的基础上研究了噪声对集合种群的稳定性的影响. 应用Fokker-Planck方程得到了系统的稳态概率分布函数和平均灭绝时间. 经过数值分析,结果如下: 无关联(λ=0 λ为加性噪声和乘性噪声之间的关联强度)时, 加性噪声强度α和乘性噪声强度D均弱化集合种群的稳定性; 噪声之间关联(λ≠0)时, 随着λ的增大,系统的稳定性被增强. 当-(c-e-D)²/(4c√Dα)<λ<1时, λ诱导"共振抑制"现象. D存在一个临界值, 小于临界值时, D可以增强系统的稳定性.

Effect of noises on the stability of a metapopulation

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 (λ= 0,λis the intensity of correlation between multiplicative and additive noise),the increase of the additive noise intensityαand the multiplicative noise intensity D weaken the stability of a metapopulation;for the case ofλ≠0,λenhances the stability of a metapopulation.For—(c—e—D)2/(AcVDa) < A < 1,A 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.