带分数布朗运动的随机时滞Lotka-Volterra模型的有界性

Boundedness of Stochastic Delay Lotka-Volterra Model with Fractional Brownian Motion

文章给出了带有分数布朗运动的随机延迟LotKa-Volterra模型dx(t)=diag(x1(t),…,xn(t))[(b+Ax(t-τ)dt+σx(t)dBtH],利用It形式,Barkholder-Davis-Gundy不等式,Chebyshev不等式,讨论了随机延迟LotKa-Volterra的有界性.得到的结果显示环境噪声不仅可以抑制人口爆破,而且使得其解是随机毕竟有界.

In this paper,a stochastic delay Lotka-Volterra model with fractional Brownian motion dx（t）=diag（x1（t）,…,xn（t））[（b＋Ax（t-τ）dt＋σx（t）dBHt],is established.By utilizing It formula,Barkholder-Davis-Gundy′s inequality,Chebyshev′s inequality,we discusse boundedness of stochasitc delay Lotka-Volterra model.We conclude that the environmental noise not only can suppress a potential population explosion,but will also make the sol utions to be stochastically ultimately bounded.