Edge-based strategies enhance cooperation in intertwined dynamics of cooperation and synchronization

In various ecosystems and human societies, living organisms and systems often exhibit cooperative and synchronous behaviors during survival. Recently, co-evolutionary models of cooperation and synchronization have shed light on the underlying mechanisms driving such behaviors, offering an intriguing avenue for studying these phenomena. However, current research predominantly focuses on a point-strategy decision mode, where each individual is limited to taking the same actions towards its neighbors. Such an assumption implies that an individual is unable to differentiate its neighbors and adjust its strategy accordingly, making it difficult to capture the complexity and diversity of interactive behaviors observed in reality. To this end, we introduce the interaction mode based on the edge-strategy and investigate how synchronization and cooperation co-evolve under interaction diversity. Specifically, we explore a scenario in which individuals can adopt different strategic decisions toward their neighbors based on their differences, thereby extending the traditional point strategy. Our research clarifies the positive role of interaction diversity in alleviating the evolutionary Kuramoto's dilemma. Moreover, it provides new insights and ideas for comprehending the influence of edge-strategy on the co-evolution of cooperative and synchronous behaviors.