Necessary and Sufficient Expander Properties that Lead to Synchrony in Digraphs -- Theory and Simulations

It is not hard to pin-point local conditions in digraphs that induce synchrony. We discuss the general setting with k-subsets as startups, and either one or two thresholds that activate new vertices. The problems become difficult to solve when these local properties are to be embedded in yielding a good global network. Examples and simulations are presented.