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Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches

Author

Listed:
  • Jiao, Jianjun
  • Yang, Xiaosong
  • Cai, Shaohong
  • Chen, Lansun

Abstract

In this work, we propose a delayed predator–prey model with impulsively diffusive prey between two patches. Using the stroboscopic map of the discrete dynamical system, we obtain the globally attractive condition of predator-extinction periodic solution of the system. We also obtain the permanent condition of the system by the theory of impulsive delay differential equation. Our results indicate that the discrete time delay has influence to the dynamical behaviors of the system. Finally, the numerical analysis is inserted to illustrate the results.

Suggested Citation

  • Jiao, Jianjun & Yang, Xiaosong & Cai, Shaohong & Chen, Lansun, 2009. "Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 522-532.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:3:p:522-532
    DOI: 10.1016/j.matcom.2009.07.008
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    References listed on IDEAS

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    1. Wang, Limin & Liu, Zhijun & Jinghui, & Chen, Lansun, 2007. "Impulsive diffusion in single species model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1213-1219.
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    Cited by:

    1. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    2. Zhenzhen Shi & Yaning Li & Huidong Cheng, 2019. "Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay," Mathematics, MDPI, vol. 7(7), pages 1-15, July.

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