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A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

Author

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  • Jin Yang
  • Min Zhao

Abstract

A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae‐eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small‐amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:452789
    DOI: 10.1155/2012/452789
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    References listed on IDEAS

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    Cited by:

    1. 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).
    2. Jianglin Zhao & Yong Yan, 2016. "Dynamics of a Seasonally Forced Phytoplankton‐Zooplankton Model with Impulsive Biological Control," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    3. Weiwei Zhang & Min Zhao, 2013. "Dynamical Complexity of a Spatial Phytoplankton‐Zooplankton Model with an Alternative Prey and Refuge Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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