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Global stability of interior and boundary fixed points for Lotka-Volterra systems

Baigent, SA; Hou, Z; (2012) Global stability of interior and boundary fixed points for Lotka-Volterra systems. Differential Equations and Dynamical Systems: an international journal for theory and applications , 20 (1) 53 - 66. 10.1007/s12591-012-0103-0.

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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.

Type:Article
Title:Global stability of interior and boundary fixed points for Lotka-Volterra systems
DOI:10.1007/s12591-012-0103-0
Publisher version:http://www.springerlink.com/content/k150213882w55611/
Keywords:Lotka-Volterra systems, global attractors, global repellors
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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