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Pattern selection in a ring of Kuramoto oscillators [article]

Károly Dénes, Bulcsú Sándor, Zoltán Néda
2019 arXiv   pre-print
Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods.  ...  These approaches offer a useful visual picture for understanding the complexity of the dynamics in the high dimensional state-space of this system.  ...  The system investigated by us consists of N classical Kuramoto oscillators displayed in a ring-like topology, with identical intrinsic frequencies ω 0 , each oscillator being coupled to its nearest neighbors  ... 
arXiv:1801.03028v2 fatcat:h5y3sz4iq5fljgpdcpgksy6ug4

Chimera and solitary states in 3D oscillator networks with inertia [article]

V. Maistrenko, O. Sudakov, O. Osiv
2020 arXiv   pre-print
We report the diversity of scroll wave chimeras in the three-dimensional (3D) Kuramoto model with inertia for N^3 identical phase oscillators placed in a unit 3D cube with periodic boundary conditions.  ...  In the considered model with inertia, we have found patterns which do not exist in this system without inertia. In particular, a scroll ring chimera is obtained from random initial conditions.  ...  The theoretical confirmation of the existence of a few kinds of 3D chimera states in the Kuramoto model with the cosine coupling of oscillators was done in 2019 in [20] .  ... 
arXiv:2002.08115v2 fatcat:w7v7f74lubhxjo7qgdshfeszuq

Scroll ring chimera states in oscillatory networks [article]

Volodymyr Maistrenko, Oleksandr Sudakov, Ievgen Sliusar
2021 arXiv   pre-print
We report the appearance of a scroll ring and scroll toroid chimera states from the proposed initial conditions for the Kuramoto model of coupled phase oscillators in the 3D grid topology with inertia.  ...  We analyze their properties and demonstrate, in particular, the patterns of coherent, partially coherent, and incoherent scroll ring chimera states with different structures of filaments and chaotic oscillators  ...  The first report of a stable scroll ring chimera state was done in 2020 in [21] for the Kuramoto model of coupled phase oscillators in a 3D grid topology with inertia.  ... 
arXiv:2107.09337v1 fatcat:uvlxnkj54ff6zn5hxjndlgyjn4

Chimera States on a Ring of Strongly Coupled Relaxation Oscillators

Julian Rode, Jan Frederik Totz, Enrico Fengler, Harald Engel
2019 Frontiers in Applied Mathematics and Statistics  
In chemical experiments with photo-coupled relaxation oscillators, we find that beyond weak coupling chimera patterns consist of different coexisting cluster states.  ...  Weakly coupled oscillators can exhibit seemingly incongruous synchronization patterns comprised of coherent and incoherent spatial domains known as chimera states.  ...  Our goal in this paper is to go beyond the weak coupling oscillators and describe chimera patterns on a ring of strongly coupled oscillators, which are based on chemical laboratory experiments.  ... 
doi:10.3389/fams.2019.00031 fatcat:4sgzkcmc3natjdqvgytjef63ui

Phase Patterns of Coupled Oscillators with Application to Wireless Communication [chapter]

Albert Díaz-Guilera, Alex Arenas
2008 Lecture Notes in Computer Science  
We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end  ...  Here we study the plausibility of a phase oscillators dynamical model for time division for multiple access in wireless communication networks.  ...  In particular, we were able to find the probability of selecting a given pattern under arbitrary initial conditions. In a ring of N oscillators there are (N − 1)!  ... 
doi:10.1007/978-3-540-92191-2_17 fatcat:paitb4ahrnbnpdpy3ltzkvzl3m

An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications

Ting Zhang, Mohammad R. Haider, Yehia Massoud, J. Iwan D. Alexander
2019 Electronics  
In this work, a Kuramoto model based frequency synchronization approach is utilized, and simulation results indicate less than 160 ms convergence time and close frequency match for a simplified pattern  ...  in the oscillating nodes.  ...  In [27, 28] , CMOS ring oscillators for pattern recognition were proposed. A non-Boolean ring oscillator coupled with a resistor network was proposed to function as a Hopfield network [27] .  ... 
doi:10.3390/electronics8010064 fatcat:zvuoohivenarffiojwkgvfnjqq

Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators [article]

Darka Labavic, Hildegard Meyer-Ortmanns
2017 arXiv   pre-print
We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies.  ...  Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly  ...  In both systems we select long-period orbits with repeating patterns of phase-locked motion and first check whether we find similar sequences of patterns once σ is varied.  ... 
arXiv:1705.04079v1 fatcat:6hc2n77yafgevmg55sf3ahq764

Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators

2017 Indian Academy of Sciences – Conference Series  
We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies.  ...  Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly  ...  Acknowledgements We would like to thank the organizers of the PNLD-2016 conference for a stimulating meeting from July 24-29 in Berlin.  ... 
doi:10.29195/iascs.01.01.0019 fatcat:pbwytktb3rewjcyqdxj6petsvm

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions

Michael Giver, Zahera Jabeen, Bulbul Chakraborty
2011 Physical Review E  
Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice  ...  Recent experiments in one and two-dimensional microfluidic arrays of droplets containing Belousov -Zhabotinsky reactants show a rich variety of spatial patterns [J. Phys. Chem.  ...  ACKNOWLEDGMENTS The authors acknowledge partial support of this research by the donors of the American Chemical Society Petroleum Research Fund, and by Brandeis NSF-MRSEC.  ... 
doi:10.1103/physreve.83.046206 pmid:21599269 fatcat:leozq5yjhjhdpk6qgpygt7i7c4

Linked and knotted chimera filaments in oscillatory systems

Hon Wai Lau, Jörn Davidsen
2016 Physical review. E  
of spontaneous synchrony breaking in systems of identical oscillators.  ...  In the case of complex oscillatory systems, this leads to a novel topological superstructure combining knotted filaments and synchronization defect sheets.  ...  Selected 2D cross-sections of the phase field (Fig. 1c ) show patterns similar to chimera spirals in 2D [40] , while other crosssections show features that are specific to 3D such as the chimera ring  ... 
doi:10.1103/physreve.94.010204 pmid:27575065 fatcat:fit4kjclyjezlkc2tytbneclxa

Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity

L. Timms, L. Q. English
2014 Physical Review E  
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations.  ...  We investigate the formation of spatio-temporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.  ...  Second, no pattern will now satisfy the same percentage of oscillator pairs as the simpler modes of the 1D ring.  ... 
doi:10.1103/physreve.89.032906 pmid:24730912 fatcat:n2us6gsgw5hilfombcah3ykfsy

Dense networks that do not synchronize and sparse ones that do [article]

Alex Townsend, Michael Stillman, Steven H. Strogatz
2020 arXiv   pre-print
In this regime, we ask how few edges one needs to add to a ring of n oscillators to turn it into a globally synchronizing network.  ...  We prove a partial result: all the twisted states in a ring of size n=2^m can be destabilized by adding just O(n log_2 n) edges.  ...  On the other hand, if the oscillators are arranged in a ring and sparsely coupled only to their nearest neighbors, the system can display other patterns besides inphase synchrony; these patterns take the  ... 
arXiv:1906.10627v4 fatcat:zktlkcqve5csdp26diduvmcty4

When is sync globally stable in sparse networks of identical Kuramoto oscillators? [article]

Yury Sokolov, G. Bard Ermentrout
2018 arXiv   pre-print
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks.  ...  In particular, if a graph allows a cyclic graph clustering with a sufficient number of clusters or contains a sufficiently long induced subpath without cut vertices of the graph then there is a non-synchronous  ...  We consider a simplified Kuramoto model on a sparse graph G of order n, that is, a system of n coupled oscillators, where an oscillator j is connected with a unit coupling to its neighbors in G, and the  ... 
arXiv:1812.08153v1 fatcat:hwkefknuzfarxjr36x3vv2fsue

Hub induced remote synchronization and desynchronization in complex networks of Kuramoto oscillators [article]

Vladimir Vlasov, Angelo Bifone
2016 arXiv   pre-print
Here, we show that the RS regime can exist in networks of Kuramoto oscillators, and that hub nodes can actively drive remote synchronization even in the presence of a repulsive mean field.  ...  We show that a change in the natural frequency of a hub can alone reshape synchronization patterns, and switch from direct to remote synchronization, or to hub-driven desynchronization.  ...  behavior of selected hub regions while measuring patterns of synchronized activity across the brain.  ... 
arXiv:1610.01905v1 fatcat:mxrn5j54tndnhfvmnqx6xoncmq

Interaction patterns and individual dynamics shape the way we move in synchrony [article]

Francesco Alderisio, Gianfranco Fiore, Robin N Salesse, Benoit G Bardy, Mario di Bernardo
2017 arXiv   pre-print
Here we study motor coordination (or synchronisation) in a group of individuals where participants are asked to visually coordinate an oscillatory hand motion.  ...  We observed that the coordination level of the ensemble depends on group homogeneity, as well as on the pattern of visual couplings (who looked at whom).  ...  The authors wish to thank Simon Pla (Montpellier University) for the help provided in running some of the experiments, Mathieu Gueugnon (Montpellier University) for providing some of the Matlab code necessary  ... 
arXiv:1607.02175v4 fatcat:37my6xwtzfdifmchy5vzhrjyte
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