Bellerophon state induced by the frequency–amplitude correlation in the Poincaré model

This study investigates the coupled Poincaré model with the linear frequency–amplitude correlation. As the coupling strength varies, the Bellerophon state is observed for the first time induced by a weak frequency–amplitude correlation. The Bellerophon state is characterized by the appearance of quantized, time-varying synchronous clusters before synchronization, which was previously believed to occur only in the model with the non-identical coupling or the specific frequency distribution. In this paper, we report the emergence of the Bellerophon state can be induced in the phase–amplitude system with identical coupling. As the strength of the frequency–amplitude correlation increases, the explosive phase transition emerges and the Bellerophon state disappears. Therefore, we propose a new pathway for inducing the Bellerophon state, which deepens our understanding of rich collective behavior in the real world.