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Generalized Predator‐Prey Model with Nonlinear Impulsive Control Strategy

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  • Wenjie Qin
  • Guangyao Tang
  • Sanyi Tang

Abstract

A generalized predator‐prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest‐free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator‐prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

Suggested Citation

  • Wenjie Qin & Guangyao Tang & Sanyi Tang, 2014. "Generalized Predator‐Prey Model with Nonlinear Impulsive Control Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:919242
    DOI: 10.1155/2014/919242
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    References listed on IDEAS

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    1. Tackie, Nii O. & Findlay, Henry J. & Baharanyi, Ntam, 1998. "Farm Products Marketing Practices by Limited Resource Farmers," Journal of Agribusiness, Agricultural Economics Association of Georgia, vol. 16(01), pages 1-9.
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    Cited by:

    1. Baodan Tian & Shouming Zhong & Ning Chen & Yanhong Qiu, 2014. "Dynamical Behavior for a Food‐Chain Model with Impulsive Harvest and Digest Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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