Explosive synchronization in generalized multiplex network with competitive and cooperative interlayer interactions

Explosive synchronization represents an abrupt first-order transition to coherence in coupled dynamical systems, with significant implications for real-world networks such as neural systems, power grids, and social networks. In this study, we investigate explosive synchronization in adaptive multiplex networks of an arbitrary number of layers with the coexistence of competitive and cooperative interlayer interactions, where the dynamics of a node in one layer is influenced by the coherence of its counterparts in other layers. In addition to these interlayer interactions, our model incorporates interlayer adaptive coupling that can be simultaneously cooperative and competitive. Using a generalized framework, we show that the fraction of competitive nodes fl within each layer critically impacts the synchronization dynamics. Higher fractions suppress synchronization, while lower fractions promote the degree of synchronization transition. As the number of layers increases, the hysteretic behavior associated with explosive synchronization becomes more pronounced, highlighting enhanced resilience in synchronization transitions. The analytical predictions derived from the mean-field approach align closely with the numerical simulations across networks with an arbitrary number of layers, validating the robustness of the proposed framework. This scalability across multiplex networks underscores the critical role of adaptive interdependencies in shaping synchronization patterns. These findings provide a comprehensive understanding of how multiplex architectures govern the dynamics of explosive synchronization and provide insight into controlling synchronization in complex systems.