Phase evolution and control in a synchronized Duffing-type nonlinear micro-oscillator

Synchronization, as a typical nonlinear phenomenon, has been widely observed and harnessed in various natural and engineered systems. However, the limited synchronization range restricts its potential applications. In this study, conducting comprehensive theoretical analysis and experimental exploration of the phase evolution, we gain valuable insights into the transition process from synchronization to desynchronization, focusing on the perspective of phase. For the first time, we unveil the restriction imposed on the synchronization range by the phase and propose an automatic phase tracking controller that can expand the synchronization range to encompass the entire hysteresis region of the Duffing-type nonlinear micro-resonator. This breakthrough opens up new possibilities for a broader array of applications in diverse fields.