scholarly journals Dead zones and phase reduction of coupled oscillators

2021 ◽  
Vol 31 (9) ◽  
pp. 093132
Author(s):  
Peter Ashwin ◽  
Christian Bick ◽  
Camille Poignard
Keyword(s):  
Coupled Oscillators ◽  
Dead Zones ◽  
Phase Reduction

scholarly journals High-order phase reduction for coupled oscillators

2020 ◽  
Vol 2 (1) ◽  
pp. 015005
Author(s):  
Erik Gengel ◽  
Erik Teichmann ◽  
Michael Rosenblum ◽  
Arkady Pikovsky
Keyword(s):  
Coupled Oscillators ◽  
High Order ◽  
Phase Reduction

scholarly journals Synchronization of coupled stick-slip oscillators

2014 ◽  
Vol 21 (1) ◽  
pp. 251-267 ◽  
Author(s):  
N. Sugiura ◽  
T. Hori ◽  
Y. Kawamura
Keyword(s):  
Coupled Oscillators ◽  
Weak Coupling ◽  
Reduction Method ◽  
Identical Pair ◽  
Stick Slip ◽  
Phase Reduction ◽  
Weakly Coupled ◽  
Single Oscillator ◽  
Stick Slip Motion ◽  
Slip Motion

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.

Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators

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

Phase- and Center-Manifold Reductions for Large Populations of Coupled Oscillators with Application to Non-Locally Coupled Systems

1997 ◽  
Vol 07 (04) ◽  
pp. 789-805 ◽  
Author(s):  
Yoshiki Kuramoto
Keyword(s):  
Coupled Oscillators ◽  
Center Manifold ◽  
Coupled Systems ◽  
Center Manifold Reduction ◽  
Reduction Techniques ◽  
Phase Reduction ◽  
Large Populations ◽  
Large Systems ◽  
Model Equations ◽  
Manifold Reduction

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.

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