Hierarchy, Graph Conductance, and the Essential Synchronization Backbone
Here is a link to my PhD dissertation in Physics at 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.
This page will provide some additional figures and GIFs to supplement the linked document, and will grow over time, but for now…
Below is a GIF showing the greedy algorithm process for approximating a Greedy-ESB for 50 Rossler attractors linearly coupled through their x-components on an ER graph with p=0.3. The resulting network is best described as an entangled network (Donetti et. al. 2005).
The link-based approximation algorithm estimating an ESB of a collection of 50 Rossler attractors coupled through their x-components. The result displaying both pendant vertices and large interwoven central cycles is indicative of a system having a bounded interval with negative MSF, where the ratio of end points is relatively large.