Stability in distribution of a stochastic hybrid competitive Lotka-Volterra model with Lévy jumps

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• 作者：Yu Zhao^a ; ^c ; Sanling Yuan ; ^b ; ^{math-ysling@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{sanling@usst.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lotka&ndash ; Volterra model ; Regime-switching diffusion ; Lé ; vy jumps ; Invariant probability measure
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：85
• 期：Complete
• 页码：98-109
• 全文大小：638 K

文摘

Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.