In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results. The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic oscillators are presented. The theoretical results say that linearly coupled identical harmonic oscillators synchronize for any frequency of oscillation. For nonlinearly coupled identical harmonic oscillators, synchronization is shown to occur at large enough frequency values. In the second part, the simulator and simulation results are presented. A GUI is designed in MATLAB to run the simulations. In the simulations, synchronization of coupled harmonic oscillators are studied according to different coupling strength values, different frequency values, different coupling graph types (e.g. all-to-all, ring, tree) and different coupling function types (e.g. linear, saturation, cubic). The simulation results do not only support the theoretical part of the thesis but also give some idea about the part of the synchronization of coupled harmonic oscillators uncovered by theory.

This diploma thesis deals with numerical simulations of the optical response of plasmonic infrared antennas placed on silicon substrates with thin film of silicon dioxide and subsequently with fitting of scattering spectra by model of coupled harmonic oscillators. In this work, we study an influence of length of antennas on the strength of coupling of localized surface plasmons in the antennas with phonons in silicon dioxide film. Also, the influence of silicon dioxide film thickness on this coupling is investigated.

The field of coupled resonant systems is a rich research area with enumerable real-world applications, including the fields of neural computing and pattern recognition, energy harvesting, and even modeling the behavior of certain types of biological systems. This work is primarily focused on the study of the behaviors of two subsets of this field: large networks of globally coupled resonators (which, in this work, refers to passive, damped resonant elements which require external stimulus) and smaller networks of oscillators (referring to active devices capable of self-sustained motion), which are coupled through a network of light-sensitive resistive elements. In the case of the former, we begin by developing an analytical and experimental framework to examine the behaviors of this system under various conditions, such as different coupling modalities and element-level parametric mistunings. Once a proper understanding of the dynamics of these systems has been established, we go on to develop the system into a single-input, single-output, multi-analyte volatile organic compound sensor. For the study of oscillator networks, we begin by building a device which utilizes a network of Colpitts oscillators, coupled through a series of color-filtered CdSe photocells. We then establish that through the analysis of particular emergent behaviors (most notably, frequency locking within the network), this type of system may show promise as a threshold color sensor. By exploiting these behaviors, this type of system may find applications in neuromorphic computing (particularly in optical pattern recognition).