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Synchronization patterns in rings of time-delayed Kuramoto oscillators [article]

Károly Dénes, Bulcsú Sándor, Zoltán Néda
2020 arXiv   pre-print
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling.  ...  The size of the attraction basins is numerically investigated. These sizes are changing periodically over several orders of magnitude as the parameters of the model are varied.  ...  [9] in the case of delay coupled rings of oscillators with Gaussian white noise.  ... 
arXiv:2003.14369v1 fatcat:essoqeamnjcplfceubena3uyjy

Synchronization properties of network motifs: Influence of coupling delay and symmetry

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, I. Fischer
2008 Chaos  
In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators.  ...  In this paper we study the synchronization patterns, concentrating on periodic solutions appearing in unidirectional rings, bidirectional rings and open chains of Kuramoto oscillators; patterns of interconnectedness  ...  NETWORKS OF KURAMOTO OSCILLATORS WITH TIME DELAY In our analysis, a Kuramoto system is used to describe the oscillatory dynamics of each node in the network.  ... 
doi:10.1063/1.2953582 pmid:19045490 fatcat:fdejacy7kneopiwdkkffufrofu

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  
Weakly coupled oscillators can exhibit seemingly incongruous synchronization patterns comprised of coherent and incoherent spatial domains known as chimera states.  ...  In chemical experiments with photo-coupled relaxation oscillators, we find that beyond weak coupling chimera patterns consist of different coexisting cluster states.  ...  the time delay τ in the coupling.  ... 
doi:10.3389/fams.2019.00031 fatcat:4sgzkcmc3natjdqvgytjef63ui

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

L. Timms, L. Q. English
2014 Physical Review E  
When time-delay and learning effects combine, novel synchronization phenomena are observed.  ...  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.  ...  This definition of synchronization and the use of phase offset will allow us to consistently capture the spatial patterns which may form in response to time delays.  ... 
doi:10.1103/physreve.89.032906 pmid:24730912 fatcat:n2us6gsgw5hilfombcah3ykfsy

Synchronization of frustrated phase oscillators in the small-world networks [article]

Esmaeil Mahdavi, Mina Zarei, Farhad Shahbazi
2022 arXiv   pre-print
We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks.  ...  We find that, unlike random networks, phase-shift could enhance the synchronization in small-world networks.  ...  Moreover, it has been shown that noise [16, 17] and time delay [18] can enhance synchronization in the SW networks by washing out those phase-locked patterns.  ... 
arXiv:2205.08849v1 fatcat:sp2jj7pckzfpbexv5gnrc3jjuy

Stochastic switching in delay-coupled oscillators

Otti D'Huys, Thomas Jüngling, Wolfgang Kinzel
2014 Physical Review E  
In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay.  ...  Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns.  ...  T.J. acknowledges support by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).  ... 
doi:10.1103/physreve.90.032918 pmid:25314515 fatcat:pjnxnkahkjc3pprfwtne4ldiou

Control of amplitude chimeras by time delay in oscillator networks

Aleksandar Gjurchinovski, Eckehard Schöll, Anna Zakharova
2017 Physical review. E  
We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent  ...  To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter.  ...  Acknowledgment This work was supported by DFG in the framework of SFB 910. We thank Sarah Loos, Julien Siebert, and Carolin Wille for helpful discussions.  ... 
doi:10.1103/physreve.95.042218 pmid:28505829 fatcat:w6dazlk2efgujpcwwmkr7ss3ia

Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions

Mahesh Wickramasinghe, István Z. Kiss
2014 Physical Chemistry, Chemical Physics - PCCP  
Oscillatory Ni dissolution reaction in a nonlocally coupled network of reaction sites produces a chimera pattern.  ...  Acknowledgement is made to President's Research Fund of Saint Louis University for support of this research.  ...  (b) Frequency of oscillators along the chain. (c) Kuramoto order parameter vs. time. (d) Phases of oscillators relative to the mean field phase.  ... 
doi:10.1039/c4cp02249a pmid:25069401 fatcat:anteri6cwrh2xoiibhumakjmey

Analysis and observation of moving domain fronts in a ring of coupled electronic self-oscillators

L. Q. English, A. Zampetaki, P. G. Kevrekidis, K. Skowronski, C. B. Fritz, Saidou Abdoulkary
2017 Chaos  
themselves in the ring lattice.  ...  In this work, we consider a ring of coupled electronic (Wien-bridge) oscillators from a perspective combining modeling, simulation, and experimental observation.  ...  ACKNOWLEDGMENTS We thank David Mertens for some helpful early discussions about oscillator ring lattices.  ... 
doi:10.1063/1.5009088 pmid:29092454 fatcat:skjjdfrgnng45ditt5fqwq2pwm

On Synchronization of Coupled Hopf-Kuramoto Oscillators with Phase Delays [article]

Soon-Jo Chung, Jean-Jacques Slotine
2010 arXiv   pre-print
Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.  ...  This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators  ...  Since the phase dynamic model of Hopf oscillators resembles the Kuramoto model, we can also extend the new synchronization results with time-varying or noisy natural frequencies and phase delays to Hopf  ... 
arXiv:1004.5366v2 fatcat:pdmbf4fafjbt3nag4bvudm7zny

Amplitude and phase effects on the synchronization of delay-coupled oscillators

O. D'Huys, R. Vicente, J. Danckaert, I. Fischer
2010 Chaos  
Synchronization phenomena of interacting elements are omnipresent in nature. A coupling delay may naturally appear in the interaction between the nodes, as the propagation time of a signal.  ...  We study analytically and numerically the synchronization properties of two generic oscillators coupled with delay: the Kuramoto oscillator, which only describes the phase dynamics, and the Stuart-Landau  ...  the oscillation pattern of the amplitude and the chaotic synchronization pattern.  ... 
doi:10.1063/1.3518363 pmid:21198097 fatcat:3oq4vvdqbre6vns2ve2cctzmbi

On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

Soon-Jo Chung, Jean-Jacques Slotine
2010 49th IEEE Conference on Decision and Control (CDC)  
Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary timevarying heterogeneous frequencies and delays is derived. 49th IEEE Conference on Decision and Control  ...  This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs).  ...  Since the phase dynamic model of Hopf oscillators resembles the Kuramoto model, we can also extend the new synchronization results with time-varying or noisy natural frequencies and phase delays to Hopf  ... 
doi:10.1109/cdc.2010.5717962 dblp:conf/cdc/ChungS10 fatcat:q4cig6ozwrfz7mxe6yzd7eemyu

Heterogeneous delays in neural networks

Caglar Cakan, Judith Lehnert, Eckehard Schöll
2014 European Physical Journal B : Condensed Matter Physics  
In the case of two discrete delay times resonance effects play a major role: Depending on the ratio of the delay times, various characteristic spiking scenarios, such as coherent or asynchronous spiking  ...  For continuous delay distributions different dynamical patterns emerge depending on the width of the distribution.  ...  This work was supported by the DFG in the framework of the SFB 910.  ... 
doi:10.1140/epjb/e2014-40985-7 fatcat:mblmm5id25aenf6vbw7cwzfqui

Pattern Recognition in a Ring of Delayed Phase Oscillators [article]

Jan Philipp Pade, Serhiy Yanchuk, Liang Zhao
2014 arXiv   pre-print
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits.  ...  In particular, we show that the system possesses a multitude of periodic solutions, prove stability results and present a bifurcation analysis.  ...  The idea for encoding a pattern in a ring of delay coupled oscillators is based on a time shift transformation [36, 24] . We shortly describe it here.  ... 
arXiv:1408.4666v2 fatcat:q73qh26e65aszgrbydxnhfl7sm

Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators

Mark J Panaggio, Daniel M Abrams
2015 Nonlinearity  
A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist.  ...  Recent experiments have led to increasing interest in the origin and dynamics of these states.  ...  They also thank Ernest Montbrió, Tae-Wook Ko, Emmanuelle Tognoli, and Gautam Sethia for pointing out omissions in a previous version of this manuscript.  ... 
doi:10.1088/0951-7715/28/3/r67 fatcat:frhhrwfp7jgetbessczdl2qk3a
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