Related papers: Collective dynamical response of coupled oscillato…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical…
We consider a pair of collectively oscillating networks of dynamical elements and optimize their internetwork coupling for efficient mutual synchronization based on the phase reduction theory developed in Ref. [H. Nakao, S. Yasui, M. Ota,…
We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their…
We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is…
Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and…
We introduce an adaptation algorithm by which an ensemble of coupled oscillators with attractive and repulsive interactions is induced to adopt a prescribed synchronized state. While the performance of adaptation is controlled by measuring…
A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied in the general framework of interacting phase…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
We consider a population of globally coupled oscillators in which phase shifts in the coupling are random. We show that in the maximally disordered case, where the pairwise shifts are i.i.d. random variables, the dynamics of a large…
To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…