The concept of an Essential Synchronization Backbone (ESB) of a network-coupled dynamical system was defined during my PhD research, and in many ways it ties together my interests from across complex systems science. The synchronization of chaos on network-coupled systems is a global dynamic property that requires sufficient flow for the transfer of information about the node states to overcome the sensitivity upon initial conditions of the dynamics. If coupling is bidirectional, then the concept of graph conductance as a measure of the main bottleneck to flow becomes all important to bulk synchronization, though is not sufficient to characterize global synchronization of all nodes. If directed, then hierarchical structures become important as the concept of key players and dissemination of influencer node states take priority. My dissertation (link below) was only a beginning of an exploration of this set of concepts, but it provides a solid foundation in the context of coupling networks that are simple graphs (undirected and unweighted).

Hierarchy, Graph Conductance, and the Essential Synchronization Backbone

A dissertation for Clarkson University under the advisement of Dr. Erik Bollt with co-advisor Dr. Dani ben-Avraham

as part of the C3S2: Clarkson Center for Complex Systems Science.

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