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Zbl 1161.92048
Li, Xiaoyue; Mao, Xuerong
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation.
(English)
[J] Discrete Contin. Dyn. Syst. 24, No. 2, 523-545 (2009). ISSN 1078-0947; ISSN 1553-5231/e

Summary: We consider a non-autonomous stochastic Lotka-Volterra competitive system $$dx_i (t) = x_i(t) \Bigg[\bigg(b_i(t)-\sum_{j=1}^{n} a_{ij}(t)x_j(t)\bigg)\,dt+ \sigma_i(t) \,d B_i(t)\Bigg],$$ where $B_i(t)$ $(i=1 , 2,\dots, n)$ are independent standard Brownian motions. Some dynamical properties are discussed and sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.
MSC 2000:
*92D40 Ecology
60J65 Brownian motion
34F05 ODE with randomness

Keywords: Brownian motion; stochastic differential equation; Itô's formula; stochastic permanence; global attractivity

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