一个带白噪声的可变时滞Lotka-Volterra人口模型(英文)

A Variable Delay Lotka-Volterra Population Model with White Noise

因为人口模型经常遭遇环境噪音的影响,本文将如下Lotka-Volterra模型(t)=diag(x(t))[b+Ax(t)+Bx(t-δ(t))]随机扰动为It型随机微分方程dx(t)=diag(x(t))[(b+Ax(t)+Bx(t-δ(t)))dt+(Qx(t)+Rx(t-δ(t))dw(t)].在这个随机模型中对系数b,A,B不需任何限制,我们证明了环境噪音不仅会压制人口的爆炸还会使得方程的解随机一致有界.

Since population models are often subject to environmental noise, in this paper we stochastically perturb the Lotka-Volterra model with variable delay x（t） = diag（x（t））[b ＋ Ax（t） ＋ Bx（t - δ（t））] into the It6 form dx（t） = diag（x（t））[（b ＋ Ax（t） ＋ Bx（t -δ（t）））dt ＋ （Qx（t）＋ Rx（t - δ（t））dw（t）]. We reveal that the environmental noise will not only suppress a potential population explosion in such model but will also make the solutions to be stochastically ultimately bounded without any additional condition on the coefficients b, A, B.