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Dissertation
Synchronization and robustness of complex networks
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Autumn 2024
DOI: 10.25820/etd.007533
Abstract
This dissertation explores novel insights into the synchronization behavior of complex networks with underlying directed graphs, offering a comprehensive investigation into various aspects of network dynamics such as robustness and heterogeneity utilizing a contraction-based method. Most contraction-based studies focused on synchronization in undirected networks and diffusive couplings. However, this thesis provides necessary conditions for the existence and sufficient conditions for exponential stability in diffusive networks with directed graphs and synchronization in a specific non-diffusive network. Furthermore, the thesis analyzes the robustness of synchronization in the presence of small perturbations for both diffusive and non-diffusive coupling networks. Finally, it investigates the behavior of synchronization in a network consisting of two clusters with different intrinsic dynamics and coupling mechanisms. All theoretical results derived in this thesis are illustrated through applications to neuronal models. A comparison between the contraction-based approach with the master stability function across various applications demonstrates that the synchronization bounds provided by the contraction theory approach is notably more conservative than the master stability function method. However, the higher bounds achieve faster convergence to the synchronization solution.
Details
- Title: Subtitle
- Synchronization and robustness of complex networks
- Creators
- Fatou Kineh Ndow
- Contributors
- Zahra Aminzare (Advisor)Rodica Curtu (Committee Member)Colleen Mitchell (Committee Member)Isabel Darcy (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mathematics
- Date degree season
- Autumn 2024
- DOI
- 10.25820/etd.007533
- Publisher
- University of Iowa
- Number of pages
- x, 80 pages
- Copyright
- Copyright 2024 Fatou Kineh Ndow
- Language
- English
- Date submitted
- 12/09/2024
- Description illustrations
- Illustrations, tables, graphs, charts
- Description bibliographic
- Includes bibliographical references (pages 74-80).
- Public Abstract (ETD)
Synchronization phenomena occur almost everywhere in nature, from neurons in the brain to pancreatic beta cells to the coordinated flashing of fireflies to electric power grids. Synchronization plays a crucial role in hippocampal networks, but disruptions, such as those caused by traumatic brain injuries, can result in long-term cognitive and memory impairments. At the same time, synchronized neuronal firing is associated with pathological conditions such as epilepsy and Parkinson’s disease. Synchronization in nonlinear systems is a critical area of study with applications in both natural and engineered systems. It involves understanding how different components of a system can align their dynamics to operate in synchronization, and its robust stability remains a key focus of research. This thesis provides conditions for different types of synchronization to occur in complex networks. It also examines how well this synchronization holds up under small perturbations and in a network with two distinct clusters, each with its own intrinsic dynamics and coupling function. Examples illustrating the application of these various theories are also presented.
- Academic Unit
- Mathematics
- Record Identifier
- 9984774958702771
Metrics
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