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Dynamic analysis of a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process

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  • Ma, Chenfei
  • Zhang, Xiaofeng
  • Yuan, Rong

Abstract

In this paper, we construct and analyze a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process. By the linear chain technique, we transform the stochastic model with weak kernel into an equivalent degenerate system. Firstly, we prove the existence and uniqueness of the global positive solution to the system. Then, we get the result of extinction and persistence in the mean of the x1 and x2 respectively. In addition, the sufficient conditions for the existence of the stationary distribution to the system are established by constructing some suitable Lyapunov functions. Finally, we provide some numerical examples to illustrate theoretical results, and some conclusions and analysis are given.

Suggested Citation

  • Ma, Chenfei & Zhang, Xiaofeng & Yuan, Rong, 2025. "Dynamic analysis of a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924013171
    DOI: 10.1016/j.chaos.2024.115765
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    References listed on IDEAS

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    1. Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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    3. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
    5. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    6. A. La Cognata & D. Valenti & B. Spagnolo & A. A. Dubkov, 2010. "Two competing species in super-diffusive dynamical regimes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(2), pages 273-279, September.
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