ArticleJournal of mathematical biology2024
Structural stability of invasion graphs for Lotka-Volterra systems.
Article in Journal of mathematical biology, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Siphon Calculus and Lyapunov Functions for Generalized Lotka-Volterra Systems: A Reaction Networks Perspective.Entropy (Basel, Switzerland) · 2026Article
- A general framework for invasion cycles in ecology.Ecology · 2026Review
- Harmonic trophic potentials and memory effects in ecological dynamics in resource-limited ecosystems through the Generalized Lotka-Volterra model with biomass constraints.Theory in biosciences = Theorie in den Biowissenschaften · 2026Article
- A practical guide to characterising ecological coexistence.Biological reviews of the Cambridge Philosophical Society · 2026Review
- On Considering Unoccupied Sites in Ecological Models.Entropy (Basel, Switzerland) · 2025Article
- A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems.Journal of mathematical biology · 2025Article
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4 authors.
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Abstract
In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.
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