Stochastic resetting and hierarchical synchronization

Leiden Repository

Stochastic resetting and hierarchical synchronization

Type: Doctoral Thesis
Title: Stochastic resetting and hierarchical synchronization
Author: Meylahn, J.M.
Issue Date: 2019-09-24
Keywords: Synchronization
Kuramoto model
Stochastic resetting
Large deviation theory
Community networks
Stochastic processes
Abstract: Stochastic resetting is simple enough to be approached analytically, yet modifies stochastic processes in a non-trivial way. This modification entails making it possible that the stochastic process has to restart from its initial position at any point in time. In part I of the thesis we study the effect it has on the statistical properties of additive functionals of the Ornstein-Uhlenbeck process and Brownian motion. We are particularly interested in the change of the probabilities of rare events. The Kuramoto model has been used to model synchronization for decades, yet the effect of the underlying structure of the interactions has only recently received attention. In Part II of the thesis we study the effect of community structure in the interaction network analytically in two simple cases, namely, a hierarchical network and a two-community network. The community structure significantly enriches the model in both cases.
Promotor: Supervisor: Hollander W.T.F. den, Garlaschelli D.
Faculty: Faculty of Science
University: Leiden University
Uri: urn:isbn:9789463804752
Handle: http://hdl.handle.net/1887/78560
 

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application/pdf Full Text 9.873Mb Under embargo until 2021-03-24
application/pdf Cover 2.013Mb View/Open
application/pdf Title Pages_Contents 224.3Kb View/Open
application/pdf Chapter 1 7.588Mb View/Open
application/pdf Part I: Chapter 2 7.518Mb View/Open Full text at publisher site
application/pdf Part I: Chapter 3 7.560Mb Under embargo until 2020-09-24 Full text at publisher site
application/pdf Part II: Chapter 4 8.245Mb Under embargo until 2020-09-24 Full text at publisher site
application/pdf Part II: Chapter 5 7.818Mb Under embargo until 2021-03-24
application/pdf Part II: Chapter 6 7.911Mb Under embargo until 2021-03-24
application/pdf Bibliography 180.3Kb View/Open
application/pdf Summary in Dutch 207.1Kb View/Open
application/pdf Acknowledgements_Curriculum Vitae 159.8Kb View/Open
application/pdf Propositions 111.2Kb View/Open

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