The Essential Synchronization Backbone Problem
Please join us for an invited talk from Tyler Diggans.
Applications of the process of synchronization of networked oscillators range from chaos-based encrypted LANs to the important civil engineering problems associated with the power grid. A new optimization problem is proposed for network oscillator systems that have a stable synchronization manifold; we seek a minimal-edge spanning subgraph of the original network for which the synchronization manifold has conjugate stability. The coupling strengths may need to be adjusted and the time to synchronization may change wildly, but the goal is stability as measured by the Master Stability Function formalism. The solution space of this simple problem elucidates an interesting relationship between the property of graph conductance and the formation of hierarchies in functional network structures. For simple (non-chaotic) oscillator models, the solution space consists of all spanning trees of the original network, and we briefly discuss unpublished work on generating spanning trees of a well-studied complex network model called the (u,v)-flower graph. The majority of the talk will feature chaotic oscillator systems, which can be thought of as collections of information generators, where the process of synchronization becomes a process of sharing and exchanging information. Depending on the Lyapunov exponent of the oscillators a number of feedback loops are required to enable synchronization, and we consider this feature through symbolic dynamics. We seek to quantify the required information flow for synchronization to occur as a function of the topological entropy of the oscillators in question. This is still ongoing research and will be the bulk of my dissertation for a PhD in Physics (currently projected graduation is May 2022).
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- Date: 15 Dec 2021
- Time: 02:00 PM to 02:45 PM
- All times are (GMT-05:00) US/Eastern
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Speakers
Tyler Diggans
Biography:
- Tyler Diggans received a BS in Physics and Mathematics (2009) and an MS in Mathematics (2011) from Northern Arizona University (NAU) in Flagstaff, AZ, where his initial research focused on both computational material science and numerical/symmetry analysis of systems of PDE. He then taught math as an instructor for four years at NAU before returning to school to begin a PhD in Quantum Simulation at Tulane University. However, growing weary of increased specialization, a new found interest in Complexity Science prompted him to accept a job as a mathematician at AFRL in 2016. After some initial work on applying machine learning to the problem of space object tracking, he was accepted into the AF Civilian Academic Degree Program in 2019 and returned to school full time at Clarkson University to complete his PhD in Physics under the direction of Dr. Erik Bollt and co-advisor Dr. Dani ben-Avraham. Since then he has been exploring the origins of hierarchy in complex networks with a particular focus on the role of graph conductance. He has published a couple of network generative models for hierarchical complex networks and is now exploring the concept of hierarchy through problems at the intersection of dynamical systems, information theory, and network science.