Completely integrable replicator dynamics associated to competitive networks

Joshua Paik, Christopher Griffin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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)10.1073/pnas.1014428108] produces quasiperiodic dynamics.

Original languageEnglish (US)
Article numberL052202
JournalPhysical Review E
Issue number5
StatePublished - May 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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