Clustering-based model reduction of a network of nonlinear oscillators

Raven, Anthony (2019) Clustering-based model reduction of a network of nonlinear oscillators. Bachelor's Thesis, Applied Mathematics.

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Abstract

In this thesis we study the reduction of networks of oscillators. Specifically, the oscillators are given by neuron models characterized through nonlinear differential equations. We consider modular networks, which consist of modules of nodes with directed connections to the subsequent module, essentially forming a cycle. Given the network structure we can consider a model reduction by means of clustering. We are interested in preserving some characteristic dynamical behaviour of the network when applying this model reduction. In particular, we want to preserve the stability region for traveling wave solutions, which only occurs for certain coupling strengths of the modules and the cycle structure. We find that clustering does well in approximating this stability region compared to other more trivial simplifications of the network. We find that the accuracy of the approximation depends on the similarity of the solutions of the nodes which are clustered.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Besselink, B. and Sterk, A.E.
Degree programme:	Applied Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	10 Jul 2019
Last Modified:	14 Nov 2019 13:35
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/20078

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