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

DOI10.1007/s12591-012-0103-0zbMath1267.34096OpenAlexW2090279270MaRDI QIDQ691331

Zhanyuan Hou, Stephen A. Baigent

Publication date: 30 November 2012

Published in: Differential Equations and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12591-012-0103-0

zbMATH Keywords

Lotka-Volterra systemsglobal asymptotic stabilityglobal attractorsglobal repellors

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Stability of solutions to ordinary differential equations (34D20) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (11)

On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex ⋮ On global dynamics of type-K competitive Kolmogorov differential systems ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems ⋮ Chaotic attractors in the four-dimensional Leslie-Gower competition model ⋮ Balance simplices of 3-species May-Leonard systems ⋮ Chaotic attractors in Atkinson–Allen model of four competing species ⋮ Estimating the effect of the reorganization of interactions on the adaptability of species to changing environments ⋮ On the dynamics of multi-species Ricker models admitting a carrying simplex ⋮ Permanence and universal classification of discrete-time competitive systems via the carrying simplex ⋮ Geometric method for global stability and repulsion in Kolmogorov systems ⋮ Global stability and repulsion in autonomous Kolmogorov systems

Cites Work

• Unnamed Item
• Permanence and extinction in competitive Lotka-Volterra systems with delays
• Oscillations and limit cycles in Lotka-Volterra systems with delays
• On permanence of all subsystems of competitive Lotka-Volterra systems with delays
• May Leonard systems
• A permanence theorem for replicator and Lotka-Volterra systems
• Vanishing components in autonomous competitive Lotka-Volterra systems
• Average growth and total permanence in a competitive Lotka-Volterra System
• Fixed point global attractors and repellors in competitive Lotka–Volterra systems
• Matrix Analysis
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Global attractor in autonomous competitive Lotka-Volterra systems
• Evolutionary Games and Population Dynamics
• The dynamical behaviour of type-K competitive Kolmogorov systems and its application to three-dimensional type-K competitive Lotka Volterra systems
• From local to global behavior in competitive Lotka-Volterra systems
• Global attractor in competitive Lotka–Volterra systems
• Kolmogorov vector fields with robustly permanent subsystems

This page was built for publication: Global stability of interior and boundary fixed points for Lotka-Volterra systems