Synchronization and multistability in a higher-order network of modulated laser models

The study delves into higher-order networks, extending beyond pairwise connections, using modulated laser models, and employing simplicial complexes to model non-pairwise interactions. Two coupling scenarios, linear and nonlinear diffusive functions, are explored. Our results demonstrate that the linear diffusive coupling leads to synchronization, further enhanced with multi-node interactions, and a tendency for forming synchronous clusters before complete synchrony. In contrast, nonlinear diffusive coupling results in a cluster synchronization state with oscillation death and periodic solutions, along with observed chimera and solitary states. In this scenario, the network fails to achieve complete synchrony. Regardless of the coupling function, the network exhibits different solutions within each synchronization pattern, showcasing the potential for multistability—the coexistence of stable solutions across various collective dynamics.