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Dynamical Behaviors of Stochastic Delayed One‐Predator and Two‐Competing‐Prey Systems with Holling Type IV and Crowley‐Martin Type Functional Responses

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  • Changjian Wang
  • Zuoliang Xiong
  • Rensheng He
  • Hongwei Yin

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.

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Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7676101
DOI: 10.1155/2016/7676101
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