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Dynamics of stochastic predator-prey systems with continuous time delay

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  • Zhang, Qiumei
  • Jiang, Daqing

Abstract

The present paper deals with the problem of a stochastic predator-prey model with continuous time delay. In the case that the integral kernel is the function ae−at, the persistence in the mean and extinction of this solution are derived by making use of Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Suggested Citation

  • Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007852
    DOI: 10.1016/j.chaos.2021.111431
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    References listed on IDEAS

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    1. Sheng Wang & Linshan Wang & Tengda Wei, 2018. "Optimal Harvesting for a Stochastic Predator-prey Model with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 37-68, March.
    2. D. Valenti & L. Schimansky-Geier & X. Sailer & B. Spagnolo, 2006. "Moment equations for a spatially extended system of two competing species," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 199-203, March.
    3. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    4. Das, Amartya & Samanta, G.P., 2018. "Stochastic prey–predator model with additional food for predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 121-141.
    5. 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.
    6. 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.
    7. 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.
    8. Vadillo, Fernando, 2019. "Comparing stochastic Lotka–Volterra predator-prey models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 181-189.
    9. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    10. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    11. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    12. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
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