Kuramoto model with correlation between coupling strength and natural frequency

Synchronization is one of important collective behaviors in various systems. The identification of different synchronous dynamics and types of transition between different dynamical states has drawn great interests. In this work, we study Kuramoto model in the presence of correlation between coupling strength and natural frequency. By manipulating the correlation between coupling strength and natural frequency, synchronization transition can either be the continuous type or the discontinuous one. Rich synchronous dynamics and different transitions between them can be realized by manipulating the correlation. We hope that the coupled systems with correlation between coupling strength and natural frequency could provide a general platform to investigate synchronous dynamics.