Bifurcation and stability of periodic solutions for nonlinear lattices with analytical methods

Abstract

The aim of the present thesis was to study the bifurcation and stability of periodic solutions for nonlinear lattices. At first we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations. Moreover we study the dynamics of a pair of parametrically-driven coupled SQUIDs arranged in series. We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture a ...
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Handle URL
http://hdl.handle.net/10442/hedi/36460
ND
36460
Alternative title
Διακλαδώσεις και ευστάθεια περιοδικών λύσεων μη γραμμικών πλεγμάτων με αναλυτικές μεθόδους
Author
Agaoglou, Makrina Nikolaos
Date
2015
Degree Grantor
Aristotle University Of Thessaloniki (AUTH)
Committee members
Ρόθος Βασίλειος
Κεβρεκίδης Παναγιώτης
Φρατζεσκάκης Δημήτριος
Τσιρώνης Γεώργιος
Σταυρακάκης Νικόλαος
Ιωαννίδου Θεοδώρα
Μελετλίδου Ευθυμία
Discipline
Natural Sciences
Mathematics
Keywords
Travelling waves; Melnikov Theory; Nonlinear lattices
Country
Greece
Language
English
Description
vii, 140 σ., fig., ch.
Rights and terms of use
Το έργο παρέχεται υπό τους όρους της δημόσιας άδειας του νομικού προσώπου Creative Commons Corporation:Creative Commons Αναφορά Δημιουργού Μη εμπορική Χρήση 3.0 Ελλάδα