Piecewise Linear Dynamical Systems: From Nodes to Networks

Şaylı, Mustafa (2021) Piecewise Linear Dynamical Systems: From Nodes to Networks. PhD thesis, University of Nottingham.

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Abstract

Piecewise linear (PWL) modelling has many useful applications in the applied sciences. Although the number of techniques for analysing nonsmooth systems has grown in recent years, this has typically focused on low dimensional systems and relatively little attention has been paid to networks. We aim to redress this balance with a focus on synchronous oscillatory network states. For networks with smooth nodal components, weak coupling theory, phase-amplitude reductions, and the master stability function are standard methodologies to assess the stability of the synchronous state. However, when network elements have some degree of nonsmoothness, these tools cannot be directly used and a more careful treatment is required. The work in this thesis addresses this challenge and shows how the use of saltation operators allows for an appropriate treatment of networks of PWL oscillators. This is used to augment all the aforementioned methods. The power of this formalism is illustrated by application to network problems ranging from mechanics to neuroscience.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Coombes, Stephen
Thul, Ruediger
Nicks, Rachel
Keywords: Piecewise linear modelling, PWL, dynamics, dynamical systems
Subjects: Q Science > QA Mathematics > QA440 Geometry
Q Science > QA Mathematics > QA801 Analytic mechanics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 66053
Depositing User: Sayli, Mustafa
Date Deposited: 31 Dec 2021 04:40
Last Modified: 31 Dec 2021 04:40
URI: http://eprints.nottingham.ac.uk/id/eprint/66053

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