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Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
We theoretically study the dynamics of a pair of coupled pendulums subject to a periodic temporal modulation of their oscillation frequency. Inspired from analogous developments in quantum mechanics, we anticipate dynamical localization and…
Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the…
We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A…
This study investigates the collective dynamics (phase synchronization, instantaneous frequencies synchronization and mean frequencies synchronization) in an ensemble of four nonidentical phase oscillators with repulsive coupling. We use…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…