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Formation, stability and basin of phase-locking for Kuramoto oscillators bidirectionally coupled in a ring

Xiaoxue Zhao, Zhuchun Li, Xiaoping Xue
2018 Networks and Heterogeneous Media  
We consider the dynamics of bidirectionally coupled identical Kuramoto oscillators in a ring, where each oscillator is influenced sinusoidally by two neighboring oscillator.  ...  Our purpose is to understand its dynamics in the following aspects: 1. identify all the phase-locked states (or equilibria) with stability or instability; 2. estimate the basins for stable phase-locked  ...  In this work, we study dynamical behavior of a finite group of Kuramoto oscillators bidirectionally coupled in a ring by performing nonlinear stability analysis.  ... 
doi:10.3934/nhm.2018014 fatcat:fn5ycenipzha5kzjo5454rqn2u

The Kuramoto model in complex networks

Francisco A. Rodrigues, Thomas K. DM. Peron, Peng Ji, Jürgen Kurths
2016 Physics reports  
In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators.  ...  This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators.  ...  (iii) In a bidirectional ring, where each Kuramoto oscillator is coupled to its two neighbors, the stability of N frequency-locked solutions was conducted following the same analysis in unidirectional  ... 
doi:10.1016/j.physrep.2015.10.008 fatcat:dgrjabfngrb7viafuinublmjci

Explosive transitions in complex networks' structure and dynamics: Percolation and synchronization

S. Boccaletti, J.A. Almendral, S. Guan, I. Leyva, Z. Liu, I. Sendiña-Nadal, Z. Wang, Y. Zou
2016 Physics reports  
a collective state in the networks' dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration.  ...  A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible.  ...  Acknowledgements We would like to acknowledge gratefully all colleagues with whom we maintained (and are currently maintaining) interactions and discussions on the topics covered in the report.  ... 
doi:10.1016/j.physrep.2016.10.004 fatcat:sj6t5hhrojalfokqcev6kzkkei

The synchronization of chaotic systems

S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou
2002 Physics reports  
synchronization, phase and imperfect phase synchronization.  ...  Synchronization of chaos refers to a process wherein two (or many) chaotic systems (either equivalent or nonequivalent) adjust a given property of their motion to a common behavior due to a coupling or  ...  [307] have shown frequency-locking and PS between two mutually coupled chaotic modes of an optically pumped NH 3 ring laser, and between the chaotic oscillation of a single mode ring laser and a chaotic  ... 
doi:10.1016/s0370-1573(02)00137-0 fatcat:dlahheobcngbpad6zrm23kdffq

Networks beyond pairwise interactions: Structure and dynamics

Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, Giovanni Petri
2020 Physics reports  
Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads.  ...  We conclude with a summary of empirical applications, and an outlook on current modeling and conceptual frontiers.  ...  The authors studied the existence and stability of several types of synchronized behaviors, in unidirectionally and bidirectionally coupled small rings, pairs of oscillators, and open chains.  ... 
doi:10.1016/j.physrep.2020.05.004 fatcat:pkugz4i5obainmcrwod6i4od7q

Networks beyond pairwise interactions: structure and dynamics [article]

Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, Giovanni Petri
2020 arXiv   pre-print
Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads  ...  However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their  ...  The authors studied the existence and stability of several types of synchronized behaviors, in unidirectionally and bidirectionally coupled small rings, pairs of oscillators, and open chains.  ... 
arXiv:2006.01764v1 fatcat:h4ezvequxrbyrozpjbb6lbqhj4

Spatiotemporal order out of noise

Francesc Sagués, José M. Sancho, Jordi García-Ojalvo
2007 Reviews of Modern Physics  
The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential  ...  An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described  ...  ACKNOWLEDGMENTS We thank all our colleagues who have collaborated with us in the study of noise-induced phenomena throughout the years.  ... 
doi:10.1103/revmodphys.79.829 fatcat:d73gtihm4rah5ogvkmmlhxnzke

27th Annual Computational Neuroscience Meeting (CNS*2018): Part One

2018 BMC Neuroscience  
Acknowledgements This research was supported by NIH grant NS086082 and a GSU Brains and Behavior Seed Grant (DNC), N.H. is a Brains and Behavior and Honeycutt Fellow; A.A.P. is a 2CI Neurogenomics and  ...  Alliance through the Initiative and Networking Fund of the Helmholtz Association and the Helmholtz Portfolio theme "Supercomputing and Modeling for the Human Brain" and the European Union Seventh Framework  ...  Given phased locked stimulation data, we propose a method to study the effects of stimulation along both the tremor oscillation phase axis and the tremor oscillation amplitude axis, with the goal of better  ... 
doi:10.1186/s12868-018-0452-x pmid:30373544 pmcid:PMC6205781 fatcat:xv7pgbp76zbdfksl545xof2vzy

Patterns of synchrony in complex networks of adaptively coupled oscillators [article]

Rico Berner, Technische Universität Berlin, Eckehard Schöll, Serhiy Yanchuk
2020
Following the successful application of the phenomenological model, we investigate a paradigmatic system of adaptively and globally coupled phase oscillators inspired by neuronal networks with synaptic  ...  Our numerical as well as analytical study of the phase oscillator model allows [...]  ...  Serhiy Yanchuk for introducing me to the exciting field of adaptive networks and the theory of nonlinear dynamics.  ... 
doi:10.14279/depositonce-10613 fatcat:ng35ckdlwjdp7g2w4qvi2om5jy

Symmetry-Breaking bifurcations and reservoir computing in regular oscillator networks

André Röhm, Technische Universität Berlin, Technische Universität Berlin, Kathy Lüdge
2019
A particular focus will be on the emergence of symmetry-broken states in rings of oscillators.  ...  However, because the effects of coupling and especially those connected to symmetries are in some sense universal, generic models for oscillators and lasers more than suffice for the investigations done  ...  Eckehard Schöll, Yulia Jagodzinski and Roland Aust for providing a fruitful scientific environment in the shape of the 'Collaborative Research Center 910: Control of self-organizing  ... 
doi:10.14279/depositonce-8246 fatcat:3cgtqhfmibaipcttr5prevd2b4

Synchrony and bifurcations in coupled dynamical systems and effects of time delay [article]

Jan Philipp Pade, Humboldt-Universität Zu Berlin, Humboldt-Universität Zu Berlin
2017
Subsequently, I investigate synchronous patterns in a directed ring of phase oscillators coupled with time delay.  ...  It was only in the last few years that people tried to understand the entangled relation between the coupling structure of a network, given by a (di-)graph, and the stability properties of synchronous  ...  Subsequently, I investigate synchronous patterns in a directed ring of phase oscillators coupled with time delay.  ... 
doi:10.18452/17293 fatcat:wd6u3mu37nhlpetjonzix6dl7m

Experiments on networks of coupled opto-electronic oscillators and physical random number generators [article]

Joseph David Hart
2018
A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is spontaneously broken into coherent and incoherent parts  ...  In this thesis, we report work in two areas: synchronization in networks of coupled oscillators and the evaluation of physical random number generators.  ...  One definition is that a "chimera state" is a spatio-temporal pattern in which a system of identical oscillators is split into coexisting regions of coherent (phase and frequency locked) and incoherent  ... 
doi:10.13016/jf05-uw3i fatcat:rfvwkjczxfdg3pdutdyujemucm