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Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator‐Prey Model

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  • Huidong Cheng
  • Tongqian Zhang
  • Fang Wang

Abstract

According to the integrated pest management strategies, a Holling type I functional response predator‐prey system concerning state‐dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity 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 than the existing ones for proving the existence and attractiveness of order one periodic solution.

Suggested Citation

  • Huidong Cheng & Tongqian Zhang & Fang Wang, 2012. "Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator‐Prey Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:126018
    DOI: 10.1155/2012/126018
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    References listed on IDEAS

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    1. Nie, Linfei & Teng, Zhidong & Hu, Lin & Peng, Jigen, 2009. "Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2122-2134.
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