Dynamical Behaviors of Stochastic Delayed One-Predator and Two-Competing-Prey Systems with Holling Type IV and Crowley-Martin Type Functional Responses. (17th November 2016)

• Record Type: Journal Article
• Authors: Wang, Changjian; Xiong, Zuoliang; He, Rensheng; Yin, Hongwei
• Other Names: Anderson Douglas R. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2016(2016)
• Publication Date: 2016-11-17
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2016/7676101
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper is devoted to stochastic delayed one-predator and two-competing-prey systems with two kinds of different functional responses. By establishing appropriate Lyapunov functions, the globally positive solution and stochastic boundedness are investigated. In some case, the stochastic permanence and extinction are also obtained. Moreover, sufficient conditions of the global asymptotic stability of the system are established. Finally, some numerical examples are provided to explain our conclusions.