Piecewise Linear Dynamical Systems: From Nodes to Networks
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...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2021
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| Online Access: | https://eprints.nottingham.ac.uk/66053/ |
| _version_ | 1848800291894329344 |
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| author | Şaylı, Mustafa |
| author_facet | Şaylı, Mustafa |
| author_sort | Şaylı, Mustafa |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:49:14Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-66053 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:49:14Z |
| publishDate | 2021 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-660532022-12-31T04:30:46Z https://eprints.nottingham.ac.uk/66053/ Piecewise Linear Dynamical Systems: From Nodes to Networks Şaylı, Mustafa 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. 2021-12-31 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/66053/1/Mustafa_Sayli_14298656_PhD_Thesis_Resubmission_MinorCorrections.pdf Şaylı, Mustafa (2021) Piecewise Linear Dynamical Systems: From Nodes to Networks. PhD thesis, University of Nottingham. Piecewise linear modelling PWL dynamics dynamical systems |
| spellingShingle | Piecewise linear modelling PWL dynamics dynamical systems Şaylı, Mustafa Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title | Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title_full | Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title_fullStr | Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title_full_unstemmed | Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title_short | Piecewise Linear Dynamical Systems: From Nodes to Networks |
| title_sort | piecewise linear dynamical systems: from nodes to networks |
| topic | Piecewise linear modelling PWL dynamics dynamical systems |
| url | https://eprints.nottingham.ac.uk/66053/ |