Norden, J (2021) Symmetries and Clustering in Nonlinear Network Systems. Master's Thesis / Essay, Mathematics.
|
Text
mMATH_2021_NordenJ.pdf Download (2MB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
toestemming.pdf Restricted to Registered users only Download (120kB) |
Abstract
This thesis treats network systems of diffusively coupled nonlinear oscillators and in particular, model order reduction by means of node clustering. The question whether there are any natural choices of nodes that may be clustered together such that the reduced-order model has similar dynamical features as the original one is addressed for an example network. Results on passivity-based cluster synchronization theory are reviewed. Based on this and by exploiting symmetries present in the network, a criterion is formulated which identifies groups of nodes that can be considered natural candidates for clustering. In the case of a modular directed ring network, it is demonstrated that this criterion predicts preservation of the emergence of a modular travelling wave when comparing the original and reduced-order systems. In the case that the modular travelling wave is preserved, it is demonstrated that its local stability region with respect to the system parameters is reproduced almost exactly. The results support the hypothesis that emergent dynamical features are related to the symmetries present in the network and that this can be exploited for purposes of model order reduction by node clustering.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Besselink, B. and Sterk, A.E. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 29 Jan 2021 13:16 |
| Last Modified: | 29 Jan 2021 13:16 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/23865 |
Actions (login required)
 |
View Item |