A Locally Stable Equilibria Criterion for the Generalized Lotka-Volterra
Michael Richard Livesay
TL;DR
This paper introduces a new criterion for assessing local stability in the generalized Lotka-Volterra model, linking fixed point stability to the Schur complement of community matrices, applicable to non-degenerate cases.
Contribution
It provides a novel stability criterion connecting fixed points and community matrices in the generalized Lotka-Volterra model for non-degenerate cases.
Findings
Stability of fixed points is related to the Schur complement of community matrices.
The criterion applies specifically to non-degenerate cases.
It offers a new analytical tool for ecological stability analysis.
Abstract
The main result applies to non-degenerate cases of the generalized Lotka-Volterra model. A criterion is given that relates the stability of two fixed points with the associated Schur complement of there respective community matrices.
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Taxonomy
TopicsOptimization and Variational Analysis