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Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

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  • Rensheng He
  • Zuoliang Xiong
  • Desheng Hong

Abstract

We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By the -matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.

Suggested Citation

  • Rensheng He & Zuoliang Xiong & Desheng Hong, 2016. "Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-16, July.
    • Handle: RePEc:hin:jnddns:8453175
    DOI: 10.1155/2016/8453175
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