Synchronization of an ensemble of oscillators is an emergent phenomenon present in
several complex systems, ranging from social and physical to biological and technological …

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 …

Synchronization phenomena in large populations of interacting elements are the subject of
intense research efforts in physical, biological, chemical, and social systems. A successful …

The Kuramoto model describes a large population of coupled limit-cycle oscillators whose
natural frequencies are drawn from some prescribed distribution. If the coupling strength …

The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

We review the behavior of theoretical models of excitable systems driven by Gaussian white
noise. We focus mainly on those general properties of such systems that are due to noise …

We show that there is a link between the Kuramoto paradigm and another system of
synchronized oscillators, namely an electrical power distribution grid of generators and …

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book
discusses fundamental properties of transient and stationary solutions, emphasizing the …

We show that a current-biased series array of nonidentical Josephson junctions undergoes
two transitions as a function of the spread of natural frequencies. One transition corresponds …

The circuit equations for certain series arrays of Josephson junctions can be mapped onto a
simple model originally introduced by Kuramoto [in Proceedings of the International …