Morphisms and automorphisms of skew-symmetric Lotka–Volterra systems*

Abstract

Abstract We study the basic relation between skew-symmetric Lotka–Volterra (LV) systems and graphs, both at the level of objects and morphisms, and derive a classification from it of skew-symmetric LV 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 LV systems. We also give a functorial interpretation of the results which we obtain.