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Global stability analysis of a ratio-dependent predator-prey system

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Abstract

A ratio dependent predator-prey system with Holling type III functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P. R. China

    Tie-jun Lu  (鲁铁军), Mei-juan Wang  (王美娟) & Yan Liu  (刘姸)

Authors
  1. Tie-jun Lu  (鲁铁军)
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  2. Mei-juan Wang  (王美娟)
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  3. Yan Liu  (刘姸)
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Corresponding author

Correspondence to Mei-juan Wang  (王美娟).

Additional information

Communicated by LIU Zeng-rong

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Lu, Tj., Wang, Mj. & Liu, Y. Global stability analysis of a ratio-dependent predator-prey system. Appl. Math. Mech.-Engl. Ed. 29, 495–500 (2008). https://doi.org/10.1007/s10483-008-0407-y

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  • DOI: https://doi.org/10.1007/s10483-008-0407-y

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2000 Mathematics Subject Classification

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