SINGLE INTERCONNECTION OF KURAMOTO COUPLED OSCILLATORS

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...

Classification of attractors for systems of identical coupled Kuramoto oscillators.

We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed poin...

Almost Global Synchronization of Symmetric Kuramoto Coupled Oscillators

Time Delay in the Kuramoto Model of Coupled Oscillators

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive exact formulas for the stability boundaries of the incoherent and synchronized states, as a function of the delay, in the special case where the oscillators...

Chimera states in coupled Kuramoto oscillators with inertia.

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At...