Synchronization of linearly and nonlinearly coupled harmonic oscillators

Penbegül, Ali Yetkin
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.


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Citation Formats
A. Y. Penbegül, “Synchronization of linearly and nonlinearly coupled harmonic oscillators,” M.S. - Master of Science, Middle East Technical University, 2011.