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Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy

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  • Min Zhao
  • Yanzhen Wang
  • Lansun Chen

Abstract

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.

Suggested Citation

  • Min Zhao & Yanzhen Wang & Lansun Chen, 2012. "Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, August.
    • Handle: RePEc:hin:jnljam:969425
    DOI: 10.1155/2012/969425
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    Cited by:

    1. Xinmiao An & Xiaomin Wang & Boyu Zhang, 2020. "Bimatrix Replicator Dynamics with Periodic Impulses," Dynamic Games and Applications, Springer, vol. 10(3), pages 676-694, September.
    2. Baba, Bashir Abdullahi & Bilgehan, Bulent, 2021. "Optimal control of a fractional order model for the COVID – 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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