Abstract
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.