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Periodic solutions and homoclinic bifurcation of a predator–prey system with two types of harvesting

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Abstract

In this paper, a predator–prey model with both constant rate harvesting and state dependent impulsive harvesting is analyzed. By using differential equation geometry theory and the method of successor functions, the existence, uniqueness and stability of the order one periodic solution have been studied. Sufficient conditions which guarantee the nonexistence of order k (k≥2) periodic solution are given. We also present that the system exhibits the phenomenon of homoclinic bifurcation under some parametric conditions. Finally, some numerical simulations and biological explanations are given.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11171284), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (104200510011), program for Innovative Research Team (in Science and Technology) in University of Henan Province (2010IRTSTHN006) and Sci-tech program project of Henan Province (122300410034).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, Henan, P.R. China

    Mingzhan Huang, Shouzong Liu & Xinyu Song

  2. Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, P.R. China

    Lansun Chen

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  1. Mingzhan Huang
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  2. Shouzong Liu
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  3. Xinyu Song
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  4. Lansun Chen
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Correspondence to Xinyu Song.

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Huang, M., Liu, S., Song, X. et al. Periodic solutions and homoclinic bifurcation of a predator–prey system with two types of harvesting. Nonlinear Dyn 73, 815–826 (2013). https://doi.org/10.1007/s11071-013-0834-7

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  • DOI: https://doi.org/10.1007/s11071-013-0834-7

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