The transition to phase synchronization in systems consisting of a large number (N) of coupled nonlinear oscillators via the route of phase clustering (phase synchronization among subsets of oscillators) is investigated. We elucidate the mechanism for the merger of phase clusters and find an algebraic scaling between the critical coupling parameter required for phase synchronization and N. Our ...

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with N elements can be deduced from the autocorrelation of the single delayed feedback system. Coupling a ring element to a chain of unidirecti...

We consider a general class of nonlinear dynamical systems with memory. prove under which conditions periodic perturbations allow solutions the same period. In particular, we memory kernels ?-type, give prominence to critical phenomena in past.

A nonlinear vibration system, over a span of convincing periodic motion, might break out abruptly catastrophic instability, but the lack theoretical tool has obscured prediction outbreak. This paper deploys amplitude-frequency formulation for oscillators to reveal critically important mechanism pseudo-periodic and finds quadratic force contributes pull-down phenomenon in each cycle when reaches...

The anticontinuum limit (i.e. the limit of weakly coupled oscillators) is used to obtain two surprising results. First we prove the continuation of discrete breathers of weakly interacting harmonic oscillators, provided a suitable coupling is chosen. Secondly we derive an analytical result for the wave transmission by a breather of the discrete nonlinear Schrödinger equation at weak coupling. W...