Pulse Processes on Signed Digraphs

One of the concepts that can be used to analyze interacting factors in ecological systems, and in other complex systems, is the notion of a signed digraph. This report considers the mathematical theory of predicting and controlling pulse processes in such digraphs. The authors (1) introduce the basic definitions and in particular the concept of stability under a pulse process; (2) show how classical techniques of linear analysis, combined with structural information from the digraph itself, enable one to characterize the stability and general long-term behavior of a signed digraph under a pulse process; and (3) illustrate how the theory of linear recursion sequences can be used to settle questions about pulse processes by developing the theory of stability for a special, but very important, class of digraphs known as rosettes. They also show that most of the results on signed digraphs apply to the more general concept of real-weighted digraphs.