Synchronization of Coupled Oscillators: The Taylor Expansion of the Inverse Kuramoto Map

Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies.

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show th...

Single Interconnection of Kuramoto Coupled Oscillators

In this work, we analyze the almost global synchronization property of sinusoidally coupled oscillators. In contrast with previous works, we introduce an approach that uses the strong basic facts of algebraic graph theory to prove dynamical properties of the standard symmetric Kuramoto model. We show how we can interconnect two (or several) systems via bridges, keeping the almost global synchro...

Almost Global Synchronization of Symmetric Kuramoto Coupled Oscillators

Model Checking Biological Oscillators

We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. The semantics of their interactions, parametric w.r.t. a model of synchronization, is introduced. We apply it to the Kuramoto model. Then, we introduce a logic, Kuramoto Synchronization Logic (KSL), and a model checking algorithm in order to verify collective synchronization prope...

Oscillator Synchronization

The nonlinear Kuramoto equations for n coupled oscillators are derived and studied. The oscillators are defined to be synchronized when they oscillate at the same frequency and their phases are all equal. A control-theoretic viewpoint reveals that synchronized states of Kuramoto oscillators are locally asymptotically stable if every oscillator is coupled to all others. The problem of synchroniz...