Volume 142, Number 3, May 2023
|Number of page(s)
|Fluid and nonlinear dynamics
|02 May 2023
Higher-order dynamics in the replicator equation produce a limit cycle in rock-paper-scissors
1 Applied Research Laboratory, Penn State University - University Park, PA 16802, USA
2 Beijing Institute of Mathematical Sciences and Applications - Beijing 101408, China
3 Yau Mathematical Sciences Center, Tsinghua University - Beijing 100084, China
(a) E-mail: email@example.com (corresponding author)
Received: 5 January 2023
Accepted: 17 April 2023
Recent work has shown that pairwise interactions may not be sufficient to fully model ecological dynamics in the wild. In this letter, we consider a replicator dynamic that takes both pairwise and triadic interactions into consideration using a rank-three tensor. We study these new nonlinear dynamics using a generalized rock-paper-scissors game whose dynamics are well understood in the standard replicator sense. We show that the addition of higher-order dynamics leads to the creation of a subcritical Hopf bifurcation and consequently an unstable limit cycle. It is known that this kind of behaviour cannot occur in the pairwise replicator in any three-strategy games, showing the effect higher-order interactions can have on the resulting dynamics of the system. We numerically characterize parameter regimes in which limit cycles exist and discuss possible ways to generalize this approach to studying higher-order interactions.
© 2023 The author(s)
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