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Global Stability of Interior and Boundary Fixed Points for Lotka–Volterra Systems

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Abstract

For permanent and partially permanent, uniformly bounded Lotka–Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka–Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka–Volterra system with general species–species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov technique to competitive Lotka–Volterra systems, our method does not require the existence of a carrying simplex.

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Authors and Affiliations

  1. Department of Mathematics, UCL, Gower Street, London, WC1E 6BT, UK

    Stephen Baigent

  2. Faculty of Computing, London Metropolitan University, North Campus, 166-220 Holloway Road, London, N7 8DB, UK

    Zhanyuan Hou

Authors
  1. Stephen Baigent
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  2. Zhanyuan Hou
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Correspondence to Stephen Baigent.

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Baigent, S., Hou, Z. Global Stability of Interior and Boundary Fixed Points for Lotka–Volterra Systems. Differ Equ Dyn Syst 20, 53–66 (2012). https://doi.org/10.1007/s12591-012-0103-0

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  • DOI: https://doi.org/10.1007/s12591-012-0103-0

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