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Kuramoto model with uniformly spaced frequencies:Finite-N asymptotics of the locking threshold
Bertrand Ottino-Loffler, Steven Strogatz
We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, , is large but finite, and the oscillators' natural freq…
Evolutionary game dynamics of controlled and automatic decision-making
Danielle F. P. Toupo, Steven H. Strogatz, Jonathan D. Cohen +1
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a mod…
Nonlinear Dynamics of the Rock-Paper-Scissors Game with Mutations
Danielle F. P. Toupo, Steven H. Strogatz
We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional muta…
Limit Cycles Sparked by Mutation in the Repeated Prisoner's Dilemma
Danielle F. P. Toupo, David G. Rand, Steven H. Strogatz
We explore a replicator-mutator model of the repeated Prisoner's Dilemma involving three strategies: always cooperate (ALLC), always defect (ALLD), and tit-for-tat (TFT). The dynam…
Simple model for the Darwinian transition in early evolution
Hinrich Arnoldt, Steven H. Strogatz, Marc Timme
It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic…
Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators
Kevin P. O'Keeffe, Pavel L. Krapivsky, Steven H. Strogatz
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did n…