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Stability in Distribution of a Stochastic Competitive Lotka-Volterra System with S-type Distributed Time Delays

Author

Listed:
  • Sheng Wang

    (Henan Polytechnic University)

  • Guixin Hu

    (Henan Polytechnic University)

  • Linshan Wang

    (Ocean University of China)

Abstract

This paper concerns the dynamics of a stochastic competitive Lotka-Volterra system with S-type distributed time delays. First, sufficient conditions for stability in mean and extinction of each population are obtained. Then, sufficient conditions for the stability in distribution of the solutions (SDS) to the system are established. Finally, some numerical simulations are provided to support the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-018-9615-6
    DOI: 10.1007/s11009-018-9615-6
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    References listed on IDEAS

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    1. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    2. 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.
    3. Jianguo Tan & Hongli Wang & Yongfeng Guo, 2012. "Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, July.
    4. Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, March.
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    Cited by:

    1. Marco Desogus & Beatrice Venturi, 2023. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System," JRFM, MDPI, vol. 16(3), pages 1-20, March.
    2. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Cao, Nan & Fu, Xianlong, 2023. "Stationary distribution and extinction of a Lotka–Volterra model with distribute delay and nonlinear stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Fu, Shuaiming & Luo, Jianfeng & Zhao, Yi, 2022. "Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 665-690.

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