Morphisms and automorphisms of skew-symmetric Lotka-Volterra systems

TL;DR

This paper explores the relationship between skew-symmetric Lotka-Volterra systems and graphs, providing classifications, automorphism group descriptions, and a functorial framework for understanding their structure and symmetries.

Contribution

It introduces the concept of decloning for graphs and Lotka-Volterra systems, offering a new classification method and a functorial interpretation of their automorphisms.

Findings

Classification of systems via graphs and irreducible weighted graphs

Description of automorphism groups of these systems

Introduction of decloning as a key concept

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.