Disorder induces explosive synchronization

Skardal, Per Sebastian; Arenas, Àlex

doi:10.1103/physreve.89.062811

Cited by 63 publications

(75 citation statements)

References 44 publications

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“…(1) for = 0 and 15 on a network of size N = 1000 constructed using the configuration model [38]. We note that, similar to the C. elegans network and the SE network, in the absence of disorder the transition from incoherence to synchronization 0.5 0.7 0.9 1. transitions can be induced for cases in which the phase transitions are continuous under the condition ω i = k i if ε is large enough [248]. The effect of addition of disorder on the order parameter r can be seen in Fig.…”

Section: B Scale-free Networkmentioning

confidence: 97%

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The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: B Scale-free Networkmentioning

confidence: 97%

“…The effect of addition of disorder to disturb the frequency assignment ω i = k i was further analyzed by Skardal and Arenas [248] for more heterogeneous structures, namely for SF and stretched exponential networks with a degree distribution given by…”

Section: -2mentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

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“…We look for the linear stability spectrum of eigenmodes around a fixed point by adding the perturbations discussed into (13), and collecting terms of order η:…”

Section: Stability Analysis and Bifurcationsmentioning

confidence: 99%

Driven synchronization in random networks of oscillators

Hindes

Myers

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns affect the types of behavior that it can produce. Thus far, modeling efforts have focused on the tendency of networks of oscillators to mutually synchronize themselves, with less emphasis on the effects of external driving. In this work we discuss the interplay between mutual and driven synchronization in networks of phase oscillators of the Kuramoto type, and explore how the structure and emergence of such states depends on the underlying network topology for simple random networks with a given degree distribution. We find a variety of interesting dynamical behaviors, including bifurcations and bistability patterns that are qualitatively different for heterogeneous and homogeneous networks, and which are separated by a Takens-Bogdanov-Cusp singularity in the parameter region where the coupling strength between oscillators is weak. Our analysis is connected to the underlying dynamics of oscillator clusters for important states and transitions.Collective behavior of complex networks is a very active field of theoretical and practical research.In particular, models of oscillator networks have drawn much attention due to their numerous applications across diverse fields, with a particular emphasis on synchronization phenomena. Here we study the dynamics of coupled oscillators, subject to periodic forcing, on random networks with different degrees of connectivity, and uncover many dynamical behaviors as a few parameters are varied. We find that the unfolding of synchronized states, and the possibility of bistability among them, differs for networks depending on how heterogeneous the degree of local connectivity is. This is explained through a combination of analytic and numerical results.

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“…Our approach is narrowly confined to how random interactions lead to some form of weak emergence due to feedbacks 6,28,50 . Even though noise provides additional degree's of freedom that are important for adaption 17 , it has been shown that by adding uncorrelated noise to oscillators one can induced explosive synchronization, i.e., very sharp phase transitions 76,98 . Barabási and Albert show that for sufficiently heterogeneous network topologies, simple correlations can induce explosive phase transitions 15 .…”

Section: Emergencementioning

confidence: 99%

Hierarchical Causality in Financial Economics

Wilcox

Gebbie

2014

SSRN Journal

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Hierarchical analysis is considered and a multilevel model is presented in order to explore causality, chance and complexity in financial economics. A coupled system of models is used to describe multilevel interactions, consistent with market data: the lowest level is occupied by agents generating the prices of individual traded assets; the next level entails aggregation of stocks into markets; the third level combines shared risk factors with information variables and bottom-up, agent-generated structure, consistent with conditions for no-arbitrage pricing theory; the fourth level describes market factors which originate in the greater economy and the highest levels are described by regulated market structure and the customs and ethics which define the nature of acceptable transactions. A mechanism for emergence or innovation is considered and causal sources are discussed in terms of five causation classes.

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Disorder induces explosive synchronization

Cited by 63 publications

References 44 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Driven synchronization in random networks of oscillators

Hierarchical Causality in Financial Economics

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