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The Effects of Resource Limitation on a Predator-Prey Model with Control Measures as Nonlinear Pulses

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  • Wenjie Qin
  • Sanyi Tang
  • Robert A. Cheke

Abstract

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.

Suggested Citation

  • Wenjie Qin & Sanyi Tang & Robert A. Cheke, 2014. "The Effects of Resource Limitation on a Predator-Prey Model with Control Measures as Nonlinear Pulses," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-13, March.
    • Handle: RePEc:hin:jnlmpe:450935
    DOI: 10.1155/2014/450935
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    Cited by:

    1. Ming Liu & Linyi Ma & Dongpo Hu, 2024. "Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting," Mathematics, MDPI, vol. 12(18), pages 1-44, September.
    2. Wenjie Qin & Zhengjun Dong & Lidong Huang, 2024. "Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies," Mathematics, MDPI, vol. 12(7), pages 1-25, March.

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