The anomalous phase transition in coupled networks of noisy rotators with higher-order interaction

The aim of the present study is to explore the phenomenon of phase transition in globally coupled noisy rotator networks with higher-order interactions by the derivative matching moment technique and direct simulation. To this end, we firstly take the first-order, second-order and third-order interactions into account, respectively. It is found that for given parameters, the first-order coupling drives the system from an incoherent state to normal single-cluster synchronization, while the second- and third-order couplings induce anomalous phase transition, leading to partially synchronized two-cluster and three-cluster states, respectively. Particularly, it is found that in presence of noise the stationary phase distribution manifests itself as the stochastic perturbation of the point distribution of phase of the multi-cluster synchronized states in absence of noise. With this intrinsic discovery in mind, by the deterministic mean-field analysis over a two-parameter area of higher-order strengths it is revealed that more complex clustered synchronization can be induced when multiple interactions coexist. Particularly, it is found that even the individual third-order interaction can induce different type of clustered synchronization. Furthermore, we investigate the parameter-induced stochastic resonance in this complete hypergraph model of rotators and discover that there is certain intrinsic connection between the optimal stochastic resonance parameters and the phase transition points, revealing the response characteristics of complex systems near criticality. Our conclusions should be helpful for understanding the complexity in natural and social fields.