Strong asymmetric multicluster synchrony in globally coupled simplicial complexes

In recent years, the investigation of synchronization in higher-order networks has emerged as a prominent area of research in nonlinear dynamics. In this work, we present a substantially generalized model of phase oscillators on globally coupled simplex structures that elucidate the formation mechanisms of strongly asymmetric synchronization clusters in complex systems characterized by many-body interactions. The strong asymmetric cluster synchrony involves three characteristics: (1) each cluster shows a different frequency band for the natural frequencies of the synchronized oscillators, (2) the phases of each cluster are locked to different interval sizes, and (3) the oscillators are nonuniformly distributed between the clusters. Focusing on a paradigmatic example of two coupled 2-simplex (three-body) interactions, we use the mean-field method to identify the existence of strongly asymmetric multicluster synchrony. Their solutions are analytically obtained through self-consistent equations. Our results also demonstrate, both theoretically and numerically, that the presence of asymmetric multicluster synchrony gives rise to multistability. When increasing the coupling strength, the system shows a transition to synchronization, which is then followed by synchronization fading, a complete loss of synchronization, and synchronization re-establishment. Our findings are not only limited to this case, but can also be extended to n-simplex interactions. Furthermore, we highlight that the inclusion of two-body interaction terms can disrupt the stability of the incoherent state, inducing spontaneous synchronization.