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The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect

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Abstract

In this paper, considering the strategy of integrated Pest Management (IPM), a class of two-prey two-predator system with the Ivlev-type functional response and impulsive effect at different fixed time is established. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the sufficient conditions for the system to be extinct of prey and permanence are proved. Moreover, we give two sufficient conditions for the extinction of one of two prey and remaining three species are permanent. Numerical simulation shows that there exist complex dynamics for system, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade. Lastly, a brief discussion is given.

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Authors and Affiliations

  1. Department of Mathematics, Hefei Normal University, Hefei Anhui, 230061, P.R. China

    Xingjie Wu & Genan Pan

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P.R. China

    Xingjie Wu

  3. Department of Mathematics and Computational, Huainan Normal University, Huainan Anhui, 232001, P.R. China

    Wei Du

  4. Department of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi, 541004, P.R. China

    Wentao Huang

Authors
  1. Xingjie Wu
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  2. Wei Du
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  3. Genan Pan
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  4. Wentao Huang
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Correspondence to Xingjie Wu.

Additional information

This work is supported by Guangxi Science Foundation (No. 0575092), Natural Science Program of Anhui Higher Education Institution under Grant (No. KJ2010B164, KJ2012Z382), and Major Project of Hefei Normal University under Grant (No. 2010KJ04ZD).

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Wu, X., Du, W., Pan, G. et al. The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect. Indian J Pure Appl Math 44, 1–27 (2013). https://doi.org/10.1007/s13226-013-0001-3

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  • DOI: https://doi.org/10.1007/s13226-013-0001-3

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