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Predator–prey system with strong Allee effect in prey

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Abstract

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Jinfeng Wang & Junjie Wei

  2. Y.Y. Tseng Functional Analysis Research Center, Harbin Normal University, Harbin, 150025, Heilongjiang, People’s Republic of China

    Jinfeng Wang & Junping Shi

  3. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Junping Shi

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  1. Jinfeng Wang
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  2. Junping Shi
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  3. Junjie Wei
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Correspondence to Junjie Wei.

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This research is supported by the National Natural Science Foundation of China (No 10771045, 10671049) and Program of Excellent Team in HIT, National Science Foundation of US, and Longjiang professorship of Department of Education of Heilongjiang Province.

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Wang, J., Shi, J. & Wei, J. Predator–prey system with strong Allee effect in prey. J. Math. Biol. 62, 291–331 (2011). https://doi.org/10.1007/s00285-010-0332-1

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  • DOI: https://doi.org/10.1007/s00285-010-0332-1

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