Many biological and neural systems can be seen as networks of interacting periodic
processes. Importantly, their functionality, ie, whether these networks can perform their …

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

Transport phenomena in spatially periodic systems far from thermal equilibrium are
considered. The main emphasis is put on directed transport in so-called Brownian motors …

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 …

We show that series arrays of N identical overdamped Josephson junctions have extremely
degenerate dynamics. In particular, we prove that such arrays have N− 3 constants of motion …

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 …

We present a framework for analysing arbitrary networks of identical dissipative oscillators
assuming weak coupling. Using the symmetry of the network, we find dynamically invariant …

Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-
forming systems, such as neural networks, convecting fluids, laser arrays and coupled …

We discuss the asymptotic formation and nonlinear orbital stability of phase-locked states
arising from the ensemble of non-identical Kuramoto oscillators. We provide an explicit …

Systems of N identical phase oscillators with global sinusoidal coupling are known to
display low-dimensional dynamics. Although this phenomenon was first observed about 20 …