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The dynamical behaviors of a food chain model with impulsive effect and Ivlev functional response

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  • Xiang, Zhongyi
  • Song, Xinyu

Abstract

In this paper, a food chain model with Ivlev functional response and impulsive effect of top predator is investigated. Conditions for extinction of mid-level predator are given. By using the Floquet theory of linear τ-period impulsive differential equation and small amplitude perturbation skills, we show that the lowest-level prey and the mid-level predator extinction periodic solution is unstable, while the mid-level predator eradication periodic solution is stable, and meanwhile, we prove that the system is permanent if the impulsive period is larger than some critical value. Furthermore, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which displays complicated behavior including a sequence of direct and inverse cascade of period doubling, period halfing as well as chaos.

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  • Xiang, Zhongyi & Song, Xinyu, 2009. "The dynamical behaviors of a food chain model with impulsive effect and Ivlev functional response," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2282-2293.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2282-2293
    DOI: 10.1016/j.chaos.2007.06.124
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    References listed on IDEAS

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    1. Xiang, Zhongyi & Song, Xinyu, 2006. "Extinction and permanence of a two-prey two-predator system with impulsive on the predator," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1121-1136.
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    Cited by:

    1. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    2. Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.

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