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Stochastic Lotka-Volterra model with infinite delay

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  • Wan, Li
  • Zhou, Qinghua

Abstract

The stochastic Lotka-Volterra system with infinite delay is studied. We show that the solution of such a system is a positive solution without explosion and give the conditions to guarantee stochastic ultimate boundedness of the solution.

Suggested Citation

  • Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:698-706
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    Cited by:

    1. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    2. Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    3. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2018. "Stability in distribution of a stochastic predator–prey system with S-type distributed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 919-930.
    4. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2020. "Permanence of hybrid competitive Lotka–Volterra system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. 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.

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