Percolation and synchronization are two phase transitions that have been extensively
studied since already long ago. A classic result is that, in the vast majority of cases, these …

In this paper, we discuss recent progress in research of ensembles of mean field coupled
oscillators. Without an ambition to present a comprehensive review, we outline most …

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in
which synchronous and asynchronous oscillation coexist. This state of broken symmetry …

The synchronization of coupled oscillators is a fascinating manifestation of self-organization
that nature uses to orchestrate essential processes of life, such as the beating of the heart …

Populations of coupled oscillators may exhibit two coexisting subpopulations, one with
synchronized oscillations and the other with unsynchronized oscillations, even though all of …

Chimera states are self-organized spatiotemporal patterns of coexisting coherence and
incoherence. We give an overview of the main mathematical methods used in studies of …

Synchronization phenomena represent one of the central issues in the modern research, in
particular, on nonlinear dynamics, network science, and statistical physics with applications …

Networks of identical, symmetrically coupled oscillators can spontaneously split into
synchronized and desynchronized subpopulations. Such chimera states were discovered in …

Time-delayed systems are found to display remarkable temporal patterns the dynamics of
which split into regular and chaotic components repeating at the interval of a delay. This …

Chimera states, representing a spontaneous breakup of a population of identical oscillators
that are identically coupled, into subpopulations displaying synchronized and …