Zwerwer, L.R. (2017) Time frequency analysis of the Kuramoto model. Master's Thesis / Essay, Mathematics.
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Abstract
In this research we study the synchronization of the Kuramoto model. We discuss a threshold for synchronization of this model. Moreover, we discuss the stability of different states and reduce the Kuramoto model to a three dimensional system. Furthermore, we discuss chimera states. This is a state in which an array of oscillators splits into two (or more) groups; one group is completely synchronized in phase and frequency, while the other group is incoherent. For the chimera states we discuss a reduced system. Moreover, we discuss the bifurcations of chimera states. Subsequently we look deeper into the use of the wavelet transform as a tool to detect synchronization. Furthermore, we discuss time frequency plots for different situations. Using the time frequency analysis we confirm the threshold for synchronization and gain more insight into the process of synchronization. Finally, we discuss disadvantages and advantages of the wavelet transform as a tool to detect synchronization.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:31 |
| Last Modified: | 15 Feb 2018 08:31 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/15711 |
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