Differential Equations and Dynamical Systems

, Volume 20, Issue 1, pp 53–66

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

Original Research

DOI: 10.1007/s12591-012-0103-0

Cite this article as:
Baigent, S. & Hou, Z. Differ Equ Dyn Syst (2012) 20: 53. doi:10.1007/s12591-012-0103-0

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.

Keywords

Lotka–Volterra systemsGlobal attractorsGlobal repellorsGlobal asymptotic stability

Mathematics Subject Classification (2000)

34D0534D2034C1192D25

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