Partial permanence and extinction on stochastic Lotka-Volterra competitive systems

[摘要] This paper discusses an autonomous competitive Lotka-Volterra model in random environments. The contributions of this paper are as follows. (a) Some sufficient conditions for partial permanence and extinction on this system are established; (b) By using some novel techniques, the conditions imposed on permanence and extinction of one-species are weakened. Finally, a numerical experiment is conducted to validate the theoretical findings.

[学科分类] 数学（综合）

[关键词] Lotka-Volterra model;random environments;Brownian motions;Itô formula;persistence in mean;extinction