Journal ArticleDOI
Bistability of patterns of synchrony in Kuramoto oscillators with inertia
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TLDR
The dynamics, that governs the bistability of the phase shifts, is described by a driven pendulum equation and the implications of these stability results to the stability of chimeras are discussed.Abstract:
We study the co-existence of stable patterns of synchrony in two coupled populations of identical Kuramoto oscillators with inertia. The two populations have different sizes and can split into two clusters where the oscillators synchronize within a cluster while there is a phase shift between the dynamics of the two clusters. Due to the presence of inertia, which increases the dimensionality of the oscillator dynamics, this phase shift can oscillate, inducing a breathing cluster pattern. We derive analytical conditions for the co-existence of stable two-cluster patterns with constant and oscillating phase shifts. We demonstrate that the dynamics, that governs the bistability of the phase shifts, is described by a driven pendulum equation. We also discuss the implications of our stability results to the stability of chimeras.read more
Citations
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A First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems
TL;DR: In this article, the collective behavior of a set of coupled damped driven pendula with finite inertia was analyzed, and it was shown that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia.
Journal ArticleDOI
Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators
TL;DR: In this article, the authors studied cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, and derived quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure the asymptotic stability of the cluster synchronization manifold.
Journal ArticleDOI
Introduction to focus issue: Patterns of network synchronization
TL;DR: This Focus Issue presents a selection of contributions at the forefront of developments in synchronization of coupled systems, including chimera states, phenomena determined by symmetry, remote synchronization, and asymmetry-induced synchronization.
Journal ArticleDOI
Occurrence and stability of chimera states in coupled externally excited oscillators
TL;DR: A statistical analysis is presented and sensitivity of the probability of observing chimeras to the initial conditions and parameter values is investigated, as well as in other networks of coupled forced oscillators.
Journal ArticleDOI
What adaptive neuronal networks teach us about power grids.
TL;DR: It is proved that phase oscillator models with inertia can be viewed as a particular class of adaptive networks, and the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.
References
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Journal ArticleDOI
The Kuramoto model: A simple paradigm for synchronization phenomena
TL;DR: In this paper, a review of the Kuramoto model of coupled phase oscillators is presented, with a rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years.
Journal ArticleDOI
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
TL;DR: In this article, the authors review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto's work to Crawford's recent contributions.
Journal ArticleDOI
The synchronization of chaotic systems
TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
Journal ArticleDOI
Master Stability Functions for Synchronized Coupled Systems
TL;DR: In this paper, the authors show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function, which can be tailored to one's choice of stability requirement.
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