Dynamics of a stochastic Lotka–Volterra model perturbed by white noise
- 作者：Nguyen Huu Du and Vu Hai Sam
- 关键词：Lotka– ; Volterra model ; Brownian motion ; Stochastic differential equation ; Asymptotic behavior
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2006
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：1 December 2006
- 卷：324
- 期：1
- 页码：82-97
- 文件大小：204 K
摘要
This paper continues the study of Mao et al. investigating two aspects of the equation
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] concerning with the upper-growth rate of the total quantity 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 always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower-growth rate.