Synchronization conditions for Lyapunov oscillators

Synchronization of coupled oscillators is an important problem in the analysis and control of coupled dynamical systems. Loosely speaking, oscillators are synchronous if the solutions of all individual oscillators converge towards a common periodic solution. This requirement implies properties on the ω-limit set and the asymptotic phase of the oscillator network. Both properties are barely considered in literature. Here, we consider the class of so called Lyapunov oscillators and derive novel conditions that are sufficient for synchronization of the oscillator networks.