Coevolution of Synchronization and Cooperation on Spatio-Temporal Networks

The spontaneous emergence of synchronization across various natural systems witnesses its importance in executing complex collective tasks within a population. Similarly, cooperation is a crucial behavioral mechanism for ensuring the survival of a community in numerous physical, biological, and social scenarios. Despite the evident interplay between synchronization and cooperation in many real-world systems, a rigorous investigation of their relationship has seldom been conducted. The Evolutionary Kuramoto Dilemma offers a quantitative approach to study the coevolution of cooperation and synchronization within the framework of networked interactions among populations of coupled oscillators/agents. Each individual may decide whether or not to cooperate and interact with the rest of the population in order to get synchronized. The decision is based on the benefit-to-cost ratio they accrued in the past: cooperating means contributing to the collective benefit of synchronization but also incurring the individual cost of interactions. We investigate the onset of synchronization and cooperation within this framework, emphasizing how different interaction topologies significantly influence the emerging phenomena. Following an initial investigation on static networks, our analysis shifts to spatio-temporal networks, aiming to identify the conditions under which mobile individuals and dynamical interactions promote synchronization and cooperation.