Fixed-Time Synchronization of Coupled Oscillator Networks with a Pacemaker

This paper investigates the fixed-time synchronization problem of a Kuramoto-oscillator network in the presence of a pacemaker. Based on the framework of the cyber-physical system (CPS), fixed-time synchronization criteria of such network are presented respectively for identical and non-identical oscillators. In virtue of Lyapunov stability analyses, sufficient conditions are deduced for achieving phase agreement and frequency synchronization for arbitrary initial phases and/or frequencies under distributed control strategies. Theoretical analysis shows that synchronization can be achieved in a fixed time, which is unrelated to initial phases/frequencies. Furthermore, the upper bounds of synchronization time are also obtained. Finally, the numerical simulations also verify the effectiveness of the derived results.

Automated summary

This paper investigates the fixed-time synchronization problem of a Kuramoto-oscillator network in the presence of a pacemaker. The synchronization criteria for phase agreement and frequency synchronization are presented using distributed control strategies and Lyapunov stability analysis. The upper bounds of synchronization time are obtained, and numerical simulations confirm the effectiveness of the derived results.