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Dynamic behaviors of a predator–prey model perturbed by a complex type of noises

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  • Guo, Xiaoxia
  • Zhu, Chunjuan
  • Ruan, Dehao

Abstract

This paper concerns a predator–prey model perturbed by a complex type of noises. The main difficulty is to give the threshold λ. We introduce some important lemmas and establish sufficient conditions for persistence stochastically and extinction. In fact, the conditions obtained are very close to the necessary conditions. Finally, numerical simulations and comparisons to existing literatures are given to illustrate our theoretical analysis.

Suggested Citation

  • Guo, Xiaoxia & Zhu, Chunjuan & Ruan, Dehao, 2019. "Dynamic behaviors of a predator–prey model perturbed by a complex type of noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1024-1037.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:1024-1037
    DOI: 10.1016/j.physa.2019.04.104
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    References listed on IDEAS

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    1. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    2. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
    3. 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.
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    Cited by:

    1. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Li, Shangzhi & Guo, Shangjiang, 2021. "Permanence of a stochastic prey–predator model with a general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 308-336.

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