Differential Equations and Dynamical Systems

, Volume 20, Issue 1, pp 53–66 | Cite as

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

  • Stephen BaigentEmail author
  • Zhanyuan Hou
Original Research


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.


Lotka–Volterra systems Global attractors Global repellors Global asymptotic stability 

Mathematics Subject Classification (2000)

34D05 34D20 34C11 92D25 


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2012

Authors and Affiliations

  1. 1.Department of MathematicsUCLLondonUK
  2. 2.Faculty of ComputingLondon Metropolitan UniversityLondonUK

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