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Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay

Author

Listed:
  • Wenxu Ning

    (Hubei Minzu University)

  • Zhijun Liu

    (Hubei Minzu University)

  • Lianwen Wang

    (Hubei Minzu University)

  • Ronghua Tan

    (Hubei Minzu University)

Abstract

This work is concerned with a novel stochastic competitive model with saturation effect and distributed delay, in which two coupling noise sources are incorporated and the interspecific competition delayed terms show saturation effect. A good understanding of exponential extinction, extinction, persistence in the mean and permanence in time average of two species are gained. Also, with the help of Lyapunov function and the global attraction of positive solution, we derive the existence and uniqueness of stationary distribution. Our main results reveal that the coupling noise sources can significantly change the survival results of two species and affect the existence of a unique stationary distribution.

Suggested Citation

  • Wenxu Ning & Zhijun Liu & Lianwen Wang & Ronghua Tan, 2021. "Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1435-1459, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09824-8
    DOI: 10.1007/s11009-020-09824-8
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    References listed on IDEAS

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    1. Zuo, Wenjie & Jiang, Daqing & Sun, Xinguo & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 542-559.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    3. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    4. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    5. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
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    Cited by:

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