Global Attractor in Competitive Lotka-Volterra Systems
Zhanyuan Hou
TL;DR
This paper establishes new criteria for the existence of a single global attractor in competitive Lotka-Volterra systems, determining species survival and extinction in ecological models.
Contribution
It introduces novel conditions that guarantee a unique global attractor in competitive Lotka-Volterra systems, enhancing understanding of species dynamics.
Findings
Existence of a single global attractor under new criteria
Conditions for species survival and extinction
Stability analysis of steady states
Abstract
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species will survive and stabilise at a steady state whereas the others, if any, will die out.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Dynamics and Pattern Formation · Mathematical Biology Tumor Growth