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The coexistence of a stochastic Lotka–Volterra model with two predators competing for one prey

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  • Zhang, Qiumei
  • Jiang, Daqing

Abstract

In this paper, we consider a stochastic Lotka–Volterra model with two predators competing for one prey. We give the sufficient conditions which guarantee that the principle of coexistence holds for this perturbed model via Markov semigroup theory. Furthermore, we prove that the densities of the solution can converge in L1 to an invariant density under appropriate conditions. Finally we make simulations to illustrate our analytical results.

Suggested Citation

  • Zhang, Qiumei & Jiang, Daqing, 2015. "The coexistence of a stochastic Lotka–Volterra model with two predators competing for one prey," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 288-300.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:288-300
    DOI: 10.1016/j.amc.2015.07.054
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    References listed on IDEAS

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    1. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    2. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
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    Cited by:

    1. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    2. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2018. "Stability in distribution of a stochastic predator–prey system with S-type distributed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 919-930.
    3. Sheng Wang & Guixin Hu & Linshan Wang, 2018. "Stability in Distribution of a Stochastic Competitive Lotka-Volterra System with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1241-1257, December.

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