The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter we demonstrate that the nodes in a second-order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call cluster explosive synchronization. We provide a rigorous analyt...

in this paper we obtain  exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    the methods used  to determine the exact solutions of the underlying equation are the lie group analysis  and the simplest equation method. the solutions obtained are  then plotted.

We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied SakaguchiKuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and AcebrónBonilla-Spigler models. We derive an exact so...

We study the Kuramoto transition of oscillators in random network and Barabáshi-Albert network model. In both cases, the results of numerical simulation show good coincidence with the mean-field analysis. Synchronization is a widely spreading behaviour in nature. It is seen in the firing of neurons in our brain, flushing of fireflies, and some chemical reactions. One of the great progress of th...

On the example of a nite dimensional approximation of the Kuramoto-Sivashinsky equation we show how topological methods may be successfully used in computer assisted proofs of the existence of heteroclinic connections in ordinary diierential equations.

We consider two and three phase-oscillators as in the Kuramoto model of coupled oscillators, replacing the sine wave interaction with a sawtooth wave. We show that for the case of non-uniform input-symmetric coupling strengths, the non-smooth, piecewise-linear dynamics synchronizes when the coupling strengths are large enough to overcome the differences in the natural frequencies of the oscilla...

We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-dr...