scholarly journals The conditions of full synchronization in generalized Kuramoto models [in Polish: Warunki pełnej synchronizacji w uogólnionych modelach Kuramoto]

2020 ◽  
Author(s):  
Jeremi Ochab
Keyword(s):  
Coupled Oscillators ◽  
Discrete System ◽  
Natural Frequencies ◽  
Phase Locking ◽  
Finite Size ◽  
Kuramoto Model ◽  
Winding Number ◽  
Critical Coupling ◽  
General Phase ◽  
Full Synchronization

A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finite-size systems may have many different synchronized stable solutions which are characterised by different values of the winding number. The lower bound for the critical coupling $k_c$ is given, as well as an algorithm for its exact calculation. It is shown that in general phase-locking does not lead to phase coherence in 1D.

scholarly journals Microscopic correlations in the finite-size Kuramoto model of coupled oscillators

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Franziska Peter ◽  
Chen Chris Gong ◽  
Arkady Pikovsky
Keyword(s):  
Coupled Oscillators ◽  
Finite Size ◽  
Kuramoto Model

Finite-size-induced transition in ensemble of globally coupled oscillators

1994 ◽  
Vol 95 (4) ◽  
pp. 541-544 ◽  
Author(s):  
Arkady S. Pikovsky ◽  
Katja Rateitschak ◽  
J�rgen Kurths
Keyword(s):  
Coupled Oscillators ◽  
Finite Size

Volume Bounds for the Phase-Locking Region in the Kuramoto Model

2018 ◽  
Vol 17 (1) ◽  
pp. 128-156 ◽  
Author(s):  
Jared C. Bronski ◽  
Timothy Ferguson
Keyword(s):  
Phase Locking ◽  
Kuramoto Model ◽  
The Kuramoto Model

Epistemological Aspects of Simulation Models for Decision Support

2013 ◽  
Vol 5 (2) ◽  
pp. 55-77 ◽  
Author(s):  
Anthony H. Dekker
Keyword(s):  
Coupled Oscillators ◽  
True Belief ◽  
Simulation Models ◽  
Decision Makers ◽  
Kuramoto Model ◽  
Model Parameters ◽  
Theoretical Construct ◽  
Formal Definitions ◽  
Complex Models ◽  
The Kuramoto Model

In this paper, the author explores epistemological aspects of simulation with a particular focus on using simulations to provide recommendations to managers and other decision-makers. The author presents formal definitions of knowledge (as justified true belief) and of simulation. The author shows that a simple model, the Kuramoto model of coupled-oscillators, satisfies the simulation definition (and therefore generates knowledge) through a justified mapping from the real world. The author argues that, for more complex models, such a justified mapping requires three techniques: using an appropriate and justified theoretical construct; using appropriate and justified values for model parameters; and testing or other verification processes to ensure that the mapping is correctly defined. The author illustrates these three techniques with experiments and models from the literature, including the Long House Valley model of Axtell et al., the SAFTE model of sleep, and the Segregation model of Wilensky.

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

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