scholarly journals Network dynamics of coupled oscillators and phase reduction techniques

2019 ◽  
Vol 819 ◽  
pp. 1-105 ◽  
Author(s):  
Bastian Pietras ◽  
Andreas Daffertshofer
1997 ◽  
Vol 07 (04) ◽  
pp. 789-805 ◽  
Author(s):  
Yoshiki Kuramoto

In the first half of this paper, some general ideas will be developed on how to approach mathematically large systems of coupled limit-cycle oscillators. Two representative reduction techniques, namely, the phase reduction and the center-manifold reduction will be presented for a prototypal system of biological cell assembly with periodic activity. The evolution equation derived through each reduction method is further classified into three groups according to the range of the oscillator coupling (i.e. local, global and intermediate). As a consequence, six classes of model equations are obtained. In the second half of the paper, some new results from our recent study on non-locally coupled oscillators will be reported, and the generation of anomalous turbulent fluctuations obeying a power law will be discussed in some detail.


2020 ◽  
Vol 2 (1) ◽  
pp. 015005
Author(s):  
Erik Gengel ◽  
Erik Teichmann ◽  
Michael Rosenblum ◽  
Arkady Pikovsky

2014 ◽  
Vol 21 (1) ◽  
pp. 251-267 ◽  
Author(s):  
N. Sugiura ◽  
T. Hori ◽  
Y. Kawamura

Abstract. A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical Hopf bifurcation. The two-oscillator system that has similar weakly coupled oscillators exhibits synchronization in a parameter range. The synchronization has an anti-phase nature for an identical pair. However, it tends to be more in-phase for a non-identical pair with a rather weak coupling. A system of three identical oscillators (1, 2, and 3) coupled in a line (with two springs k12=k23) exhibits synchronization with two of them (1 and 2 or 2 and 3) being nearly in-phase. These collective behaviours are systematically estimated using the phase reduction method.


SIAM Review ◽  
2019 ◽  
Vol 61 (2) ◽  
pp. 277-315 ◽  
Author(s):  
Dan Wilson ◽  
Bard Ermentrout

2021 ◽  
Vol 31 (9) ◽  
pp. 093132
Author(s):  
Peter Ashwin ◽  
Christian Bick ◽  
Camille Poignard

1978 ◽  
Vol 48 ◽  
pp. 389-390 ◽  
Author(s):  
Chr. de Vegt

AbstractReduction techniques as applied to astrometric data material tend to split up traditionally into at least two different classes according to the observational technique used, namely transit circle observations and photographic observations. Although it is not realized fully in practice at present, the application of a blockadjustment technique for all kind of catalogue reductions is suggested. The term blockadjustment shall denote in this context the common adjustment of the principal unknowns which are the positions, proper motions and certain reduction parameters modelling the systematic properties of the observational process. Especially for old epoch catalogue data we frequently meet the situation that no independent detailed information on the telescope properties and other instrumental parameters, describing for example the measuring process, is available from special calibration observations or measurements; therefore the adjustment process should be highly self-calibrating, that means: all necessary information has to be extracted from the catalogue data themselves. Successful applications of this concept have been made already in the field of aerial photogrammetry.


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