Dynamics of a stochastic Lotka-Volterra model perturbed by white noise
Dynamics of a stochastic Lotka-Volterra model perturbed by white noise
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DOI：
10.1016/j.jmaa.2005.11.064
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发表时间：
2006-12-01
影响因子：
1.3
通讯作者：
Sam, Vu Hai
中科院分区：
文献类型：
--
作者：
Du, Nguyen Huu;Sam, Vu Hai
本文继续对毛等人的研究。研究方程dx(T)=diag(x(1)(T)，...，x(N)(T))[(b+Ax(T))dt+sigma x(T)dw(T)]，t>；=0的两个方面。第一个方面略微改进了[X.Mao，S.Sabais，E.Renshaw，随机Lotka-Volterra模型的渐近行为，J.Math]中的结果。肛门。287(2003)141-156]，通过弱化对方程系数的假设，得到了物种总量的上限增长率。第二个方面是研究正解的低增长率。利用Lyapunov函数技巧和变时间方法，我们证明了总数量Sigma(N)(i=1)x(I)(T)总是访问点0的任何邻域，同时给出了这个低增长率的估计。(C)2005 Elsevier Inc.保留所有权利。
This paper continues the study of Mao et al. investigating two aspects of the equationdx(t)=diag(x(1)(t),...,x(n)(t))[(b+Ax(t))dt+sigma x(t)dW(t)], t >= 0.The first of these is to slightly improve results in [X. Mao, S. Sabais, E. Renshaw, Asymptotic behavior of stochastic Lotka-Volterra model, J. Math. Anal. 287 (2003) 141-156] conceming with the upper-growth rate of the total quantity Sigma(n)(i=1) x(i) (t) of species by weakening hypotheses posed on the coefficients of the equation. The second aspect is to investigate the lower-growth rate of the positive solutions. By using Lyapunov function technique and using a changing time method, we prove that the total quantity Sigma(n)(i=1) x(i) (t) always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower-growth rate. (c) 2005 Elsevier Inc. All rights reserved.