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Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation

Author

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  • Haihong Li
  • Daqing Jiang
  • Fuzhong Cong
  • Haixia Li

Abstract

We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.

Suggested Citation

  • Haihong Li & Daqing Jiang & Fuzhong Cong & Haixia Li, 2014. "Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    • Handle: RePEc:hin:jnlaaa:720283
    DOI: 10.1155/2014/720283
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    Cited by:

    1. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.

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