Unit:
Τομέας Πυρηνικής Φυσικής και Φυσικής Στοιχειωδών ΣωματιδίωνLibrary of the School of Science
Author:
Παναγάκου Ευαγγελία
Dissertation committee:
Φώτιος Διάκονος, Δημήτριος Φραντζεσκάκης, Δρ. Αστέρω Προβατά (ΕΚΕΦΕ Δημόκριτος)
Original Title:
Φαινόμενα Συγχρονισμού σε Πλέγματα Συζευγμένων Ταλαντωτών
Translated title:
Synchronization Phenomena in lattices of coupled oscillators
Summary:
In this PhD thesis we study synchronization phenomena and pattern formation in
reaction-diffusion systems, when many oscillators are coupled in a lattice
network or in a serial topology. The simulation methods used are the Kinetic
Monte Carlo and the Euler Numerical Integration. The system under study is the
dissipative Lattice Limit Cycle (LLC) model. We present how the system's
dynamics diverges from the predictions of the Mean Field Theory, when
restricted on low-dimensional supports, due to the spatial restrictions and to
the noise induced by the simulation method. We numerically show that when the
coupling is reactive (short or long distance) and when the reaction rates are
substituted by the corresponding effective values, then the mean concentrations
are correctly predicted by the Mean Field equations. This result doesn’t hold
when the coupling is of the long distance diffusion type, since this type of
diffusion is not taken into account in the Mean Field equations. To further
study the divergence from the Mean Field we employ the method of the abstract
weighted network for the description of the LLC system. We show that the
network degree distribution and the average clustering coefficient display
power law behavior with exponents which classify the system in the category of
scale free networks. We investigate the appearance of chimera states, i.e. of
the coexistence of coherent and incoherent oscillators of the LLC type, when
they are coupled in a ring topology. We calculate chimera characteristic
measures, such as the mean phase velocity, which verify the existence of such
states, and we study their multiplicity as the system approaches the critical
point of the Hopf bifurcation.
Keywords:
Reaction-difusion systems, Kinetic monte carlo simulations, Abstract network of the phase space, Chimera states, Coupled oscillators
Number of index pages:
xv-xix
Number of references:
175
