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Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

Author

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  • Huidong Cheng
  • Fang Wang
  • Tongqian Zhang

Abstract

According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

Suggested Citation

  • Huidong Cheng & Fang Wang & Tongqian Zhang, 2012. "Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, June.
    • Handle: RePEc:hin:jnddns:181752
    DOI: 10.1155/2012/181752
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    Cited by:

    1. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    2. Zhezhe Xin & Chunjie Xiao & Ting Hou & Xiao Shen, 2019. "Robust H ∞ -Control for Uncertain Stochastic Systems with Impulsive Effects," Mathematics, MDPI, vol. 7(12), pages 1-12, December.

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