噪声对集合种群稳定性的影响

Effect of noises on the stability of a metapopulation

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=0λ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)^(1/2))<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.

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, ,λ is the intensity of correlation between multiplicative and additive noise）, the increase of the additive noise intensity a and the multiplicative noise intensity D weaken the stability of a metapopulation; for the case of λ≠0, λ, enhances the stability of a metapopulation. For -（c - e - D）2/（4c√Da 〈 λ 〈 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.