Cluster synchronization in coupled systems with hub structure

We have investigated synchronization in coupled systems with a star-like configuration (hub structure). In a previous study, we found that the stability of cluster synchronized states can be controlled by the firing frequency of the central node in coupled Morris–Lecar neurons. In this study, two systems (a neuron model and an electric circuit) are considered to check the universality of this phenomenon. As a result, we also observe it for both systems. The sufficient condition of the occurrence of this phenomenon is the existence of the transition between in-phase and not-in-phase states in three coupled elements. When a hub network composed of such a coupling unit is constructed, we can control the appearance of synchronized states by changing the oscillation frequency of the central node.