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

Author

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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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:969425
    DOI: 10.1155/2012/969425
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    References listed on IDEAS

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    1. Zhao, Min & Yu, Hengguo & Zhu, Jun, 2009. "Effects of a population floor on the persistence of chaos in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1245-1250.
    2. Helong Liu & Houbao Xu & Jingyuan Yu & Guangtian Zhu, 2005. "Stability on coupling SIR epidemic model with vaccination," Journal of Applied Mathematics, John Wiley & Sons, vol. 2005(4), pages 301-319.
    3. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    4. Helong Liu & Houbao Xu & Jingyuan Yu & Guangtian Zhu, 2005. "Stability on coupling SIR epidemic model with vaccination," Journal of Applied Mathematics, Hindawi, vol. 2005, pages 1-19, January.
    5. Jin Yang & Min Zhao, 2012. "A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Jin Yang & Min Zhao, 2012. "A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, April.
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