Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching

被引：0
作者：
Xiuli He
Lei Liu
Quanxin Zhu
机构：
[1] Hohai University,College of Science
[2] Southeast University,School of Mathematics
[3] Nanjing Normal University,School of Mathematical Sciences and Institute of Finance and Statistics
来源：
Advances in Difference Equations | / 2017卷
关键词：
Lotka-Volterra model; random environments; Brownian motions; Itô formula; persistence in mean; extinction;
D O I：
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中图分类号：
学科分类号：
摘要：
We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By constructing a novel Lyapunov function we establish sufficient criteria on partial persistence in mean and partial extinction for the system. Finally, we provide two examples to demonstrate the feasibility and validity of our proposed methods.
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