- Letter
Completely integrable replicator dynamics associated to competitive networks
Phys. Rev. E 107, L052202 – Published 23 May, 2023
DOI: https://doi.org/10.1103/PhysRevE.107.L052202
Abstract
The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold integrable. We show this by explicitly providing conserved quantities and a Poisson structure. As a corollary, we classify all tournament replicators up to dimension 6 and most of dimension 7. As an application, we show that Fig. 1 of Allesina and Levine [Proc. Natl. Acad. Sci. USA 108, 5638 (2011)] produces quasiperiodic dynamics.
