Influence of small-world topology and time-scale in evolutionary Kuramoto dilemma

Institute of Computational Physics and Complex Systems, Lanzhou University - Lanzhou, Gansu 730000, China

^(a) wuzhx@lzu.edu.cn
^(b) guanjy@lzu.edu.cn

Received: 8 April 2018
Accepted: 18 May 2018

Abstract

We study the coevolution of synchronization and cooperation with costly interactions in small-world networks, in which each node, representing a Kuramoto oscillator, can interact (cooperate) —or not (defect)— with its neighbors. Being a cooperator will easily collect some benefits from the local synchronization but need to pay for a cost for interaction, while being a defector will be relatively difficult to reap payoffs since it would not like to align with their neighbors. To be a cooperator or not be constitutes the evolutionary Kuramoto dilemma. By extensive computer simulations, we find that when the relative cost for cooperation is low, more random topology favors the emergence of collective synchronization and cooperation. Whenever the cooperative behavior becomes costly, a high level of global synchronization can only be achieved in the typical small-world region, i.e., the underlying interaction should be not too regular, and not too random as well. Furthermore, simulation results with distinct time scale of the involved synchronization and cooperation dynamics show that both the cooperation and synchronization level of the system can be improved by increasing the relative time scale of strategy updating.