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Dynamics of a stochastic Holling–Tanner predator–prey model

Author

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  • Li, Haihong
  • Cong, Fuzhong

Abstract

In the paper, we study a stochastic Holling–Tanner predator–prey system. First, by constructing a suitable stochastic Lyapunov function we establish sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions to the system. After that, sufficient causes for extinction of the predator population is obtained. Meanwhile, we also obtain the threshold between persistence and extinction of the predator population. At last, some examples and numerical simulations are provided to illustrate our theoretical results.

Suggested Citation

  • Li, Haihong & Cong, Fuzhong, 2019. "Dynamics of a stochastic Holling–Tanner predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119310131
    DOI: 10.1016/j.physa.2019.121761
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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. Pimentel, Carlos Eduardo Hirth & Rodriguez, Pablo M. & Valencia, Leon A., 2020. "A note on a stage-specific predator–prey stochastic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    3. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution of a stochastic predator–prey system with stage structure for prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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