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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 M‐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, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:8453175
    DOI: 10.1155/2016/8453175
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    References listed on IDEAS

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    1. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar, 2015. "Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1072-1094.
    2. Ouyang, Mengqian & Li, Xiaoyue, 2015. "Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 539-559.
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