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Numerical Investigation of Finite Kuramoto model with time dependent coupling strength

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Date Issued:
2018
Abstract/Description:
Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t).
Title: Numerical Investigation of Finite Kuramoto model with time dependent coupling strength.
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Name(s): Khatiwada, Dharma Raj, author
Wille, Luc T., Thesis advisor
Florida Atlantic University, Degree grantor
Charles E. Schmidt College of Science
Department of Physics
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2018
Date Issued: 2018
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 94 p.
Language(s): English
Abstract/Description: Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t).
Identifier: FA00013120 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2018.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Synchronization
Oscillations
Nonlinear oscillators--Mathematical models
Oscillator strengths
Frequency of oscillating systems
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013120
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.