Morphisms and automorphisms of skew-symmetric Lotka-Volterra systems

2020/10/30 by Charalampos Evripidou, Charalampos A. Evripidou, Pavlos Kassotakis +4 · 2 citations
Mathematics · Physics and Astronomy · #37J35 #53D17 #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:37J35 #msc:53D17 #nlin.SI

paper · pdf · doi:10.48550/arxiv.2010.16180

40 pages

arxiv created 2020/10/30 · openalex publication_date 2020/10/30 · arxiv updated 2020/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the basic relation between skew-symmetric Lotka-Volterra systems and graphs, both at the level of objects and morphisms, and derive a classification from it of skew-symmetric Lotka-Volterra systems in terms of graphs as well as in terms of irreducible weighted graphs. We also obtain a description of their automorphism groups and of the relations which exist between these groups. The central notion introduced and used is that of decloning of graphs and of Lotka-Volterra systems. We also give a functorial interpretation of the results which we obtain.

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• On Coexistence of Conservative Replicator Dynamics with Four Strategies
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