Existence and Exact Multiplicity of Phaselocked Solutions of a Kuramoto Model of Mutually Coupled Oscillators

2015 ◽  
Vol 75 (4) ◽  
pp. 1745-1760 ◽  
Author(s):  
William C. Troy
Keyword(s):  
Coupled Oscillators ◽  
Kuramoto Model ◽  
Exact Multiplicity

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.

scholarly journals New forms of structure in ecosystems revealed with the Kuramoto model

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
John Vandermeer ◽  
Zachary Hajian-Forooshani ◽  
Nicholas Medina ◽  
Ivette Perfecto
Keyword(s):  
Natural History ◽  
Complex Systems ◽  
Coupled Oscillators ◽  
Ecological Systems ◽  
Kuramoto Model ◽  
Chaotic Orbits ◽  
The Kuramoto Model ◽  
Convection Rolls ◽  
Analytical Tools ◽  
Insight Into

Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens' simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz’ convection rolls. The analytics of oscillators may thus provide insight into the structure of ecological systems. One of the most popular analytical tools for such study is the Kuramoto model of coupled oscillators. We apply this model as a stylized vision of the dynamics of a well-studied system of pests and their enemies, to ask whether its actual natural history is reflected in the dynamics of the qualitatively instantiated Kuramoto model. Emerging from the model is a series of synchrony groups generally corresponding to subnetworks of the natural system, with an overlying chimeric structure, depending on the strength of the inter-oscillator coupling. We conclude that the Kuramoto model presents a novel window through which interesting questions about the structure of ecological systems may emerge.

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
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