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oscillator models, the solution space consists of all spanning trees of the original network, and we briefly discuss unpublished work on generating spanning trees of a well-studied complex network model called the (u,v)-flower graph.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).

Speaker(s): Tyler Diggans,

Virtual: https://events.vtools.ieee.org/m/294304