Kuramoto dilemma alleviated by optimizing connectivity and rationality

TL;DR

This paper investigates how optimizing network connectivity and individual rationality can alleviate the Kuramoto dilemma, enhancing synchronization in a coevolutionary oscillator model.

Contribution

It introduces an analysis of the impact of network degree and rationality on synchronization within a coevolutionary framework.

Findings

Maximum synchronization occurs at moderate network degrees.

Higher individual rationality influences strategy adoption and synchronization.

Optimal connectivity balances benefits and costs for oscillators.

Abstract

Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. \textbf{118}, 238301 (2017)], in which each Kuramoto oscillator can decide whether to interact-or not-with its neighbors, and all oscillators can receive some benefits from the local synchronization but those who choose to interact must pay a cost. Oscillators are allowed to update their strategies according to payoff difference, wherein the strategy of an oscillator who has obtained higher payoff is more likely to be followed. Utilizing this coevolutionary model, we find that the global synchronization level reaches the highest level when the average degree of the underlying interaction network is moderate. We also study how synchronization is affected by the individual rationality in choosing strategy.