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). / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_40932 |
| Contributors | Khatiwada, Dharma Raj (author), Wille, Luc T. (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Physics |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation, Text |
| Format | 94 p., application/pdf |
| Rights | Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder., http://rightsstatements.org/vocab/InC/1.0/ |
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