Adding connections can hinder network synchronization of time-delayed oscillators

Hart, Joseph D.; Pade, Jan Philipp; Pereira, Tiago; Murphy, Thomas E.; Roy, Rajarshi

doi:10.1103/physreve.92.022804

Cited by 30 publications

(17 citation statements)

References 32 publications

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“…The experiment consists of a network of four globally coupled identical, opto-electronic, time-delayed feedback loops, whose individual and coupled dynamics have been studied previously [25][26][27][28][29][30] . A layout of the network and a schematic of a single node are shown in Fig.…”

Section: A Experimental Apparatusmentioning

confidence: 99%

Experimental observation of chimera and cluster states in a minimal globally coupled network

Hart

Bansal

Murphy

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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143

101

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A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic optoelectronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.We provide experimental evidence of chimera and cluster synchronous states in a globally coupled network of four opto-electronic oscillators. Since this is the minimal network in which a chimera state can occur, our apparatus provides the ability to experimentally test some of the fundamental properties of chimera states. Cluster synchronization has thus far been studied independently of chimera states; however, here we present a unified approach that exploits the symmetries in the network to determine the stability of chimeras and clusters. We obtain two important results: A) we provide a first experimental demonstration that chimeras can appear in small networks, contrary to the conventional assumption that a large network with non-local coupling is necessary 1 , and B) we show that both cluster states and chimera states can be regarded as special cases of the more general phenomenon of partial synchronization. The methods apply to networks of different size and topology, opening up potential applications to chimeras and other partial synchrony patterns in real world networks such as power grids.

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Section: A Experimental Apparatusmentioning

confidence: 99%

Experimental observation of chimera and cluster states in a minimal globally coupled network

Hart

Bansal

Murphy

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

143

101

View full text Add to dashboard Cite

show abstract

“…In particular, the so-called Fiedler vector associated with the algebraic connectivity (i.e the second eigenvalue) of this matrix is of importance for spectral graph partitioning [23,33] and for synchronization [28,29]. Indeed, when the Fiedler vector has non-zero entries one can design structural changes that make synchronization unstable [27,19].…”

Section: Introductionmentioning

confidence: 99%

Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties

Poignard¹,

Pereira²,

Pade³

2018

SIAM J. Appl. Math.

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This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity) and its associated eigenvector, the so-called Fiedler vector.Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only non-zero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems.

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“…Note that ( , ) is nonnegative for all angles and displacements. Moreover, vanishes if and only if the objectives (3)- (4) are fulfilled. This means that if we find displacements and angles where = 0, the atoms of the resulting molecules fit the desired region and are sufficiently separated.…”

Section: May 2017mentioning

confidence: 99%

“…The question is how to make the lasers spontaneously behave in unison. We will illustrate the main characteristics of the phenomenon in an experiment described in [4]. The experiment consists of four coupled time-delayed optoelectronic oscillators (lasers) interacting according to a given network motif, as shown in Figure 2.…”

Section: Synchronization Of Complex Systemsmentioning

confidence: 99%

See 1 more Smart Citation

CeMEAI: The Brazilian Center and Its Mathematics Research for Industry

Birgin¹,

Cuminato²,

Martínez³

et al. 2017

Notices Amer. Math. Soc.

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Adding connections can hinder network synchronization of time-delayed oscillators

Cited by 30 publications

References 32 publications

Experimental observation of chimera and cluster states in a minimal globally coupled network

Experimental observation of chimera and cluster states in a minimal globally coupled network

Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties

CeMEAI: The Brazilian Center and Its Mathematics Research for Industry

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