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Periodic solution and heteroclinic bifurcation in a predator–prey system with Allee effect and impulsive harvesting

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Abstract

In this article, we investigate a prey– predator model with Allee effect and state-dependent impulsive harvesting. We obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system (1.2) by means of the geometry theory of semicontinuous dynamic system and the method of successor function. We also obtain that system (1.2) exhibits the phenomenon of heteroclinic bifurcation about parameter \(\alpha \). The methods used in this article are novel and prove the existence of order-1 periodic solution and heteroclinic bifurcation.

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Acknowledgments

Supported by National Natural Science Foundation of China (11301216,11171284), Fujian Provincial Natural Science Foundation of China (2012J01012), the Fujian Provincial Education Fundation (JA12198) and the Scientific Research Foundation of Jimei University of China (ZC2011003).

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Authors and Affiliations

  1. Science College, Jimei University, Xiamen , 361021, Fujian, People’s Republic of China

    Chunjin Wei

  2. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing , 100080, People’s Republic of China

    Lansun Chen

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  1. Chunjin Wei
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  2. Lansun Chen
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Correspondence to Chunjin Wei.

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Wei, C., Chen, L. Periodic solution and heteroclinic bifurcation in a predator–prey system with Allee effect and impulsive harvesting. Nonlinear Dyn 76, 1109–1117 (2014). https://doi.org/10.1007/s11071-013-1194-z

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  • DOI: https://doi.org/10.1007/s11071-013-1194-z

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