Multivaluedness in Networks: Theory

2020-03-10T00:31:46Z (GMT) by Anton van Wyk
An unexpected and somewhat surprising observation is that two counter-cascaded systems,12 satisfying the right conditions, implicitly exhibit multivaluedness from one of the outputs to the other. Based on the novel notions of immanence and transcendence, the main result presented here, gives a necessary and sufficient condition for multivaluedness to be exhibited by counter-cascaded systems. Subsequent corollaries provide further characterization of multivaluedness under specific conditions.

As an application of these theoretical results, we demonstrate how these aid in the structural complexity reduction of directed complex networks.