Supernetworks -- The Science of Complexity

I've been thinking a lot about complexity lately and recently completed an invited paper, "Supernetworks: The Science of Complexity."

In doing the research for this paper, which presents some of the highlights of methodological advances and applications over the past decade, what amazed me was how research conducted in one discipline can have major impacts in others.

Specifically, I was interested in overviewing the breadth and depth of applications of supernetworks, and associated methodologies, since I wrote the Supernetworks: Decision-Making for the Information Age book with Dr. June Dong back in 2002.

What I pleasantly discovered was that the methodology of projected dynamical systems, which I wrote a book on with Dr. Ding Zhang in 1996, results of which were also included in the second edition of my Network Economics book, is now being utilized and applied in evolutionary game theory, in neuroscience and robotics, and in ecological predator-prey networks! Projected dynamical systems (unlike classical dynamical systems) can handle constraints underlying dynamical systems and the theory allows for the investigation of qualitative properties, including stability of systems, and has associated with it appropriate algorithmic schemes.

Our book, Projected Dynamical Systems and Variational Inequalities with Applications, was the second volume in the International Series in Operations Research & Management Science. As reported in the book (and since), my collaborators and I have used projected dynamical systems to model dynamic traffic problems, dynamic supply chain networks and financial networks, electric power generation and distribution systems, and a variety of spatial and aspatial economic problems.

Sometimes it may take awhile for a methodology developed in one discipline to be discovered by other disciplines but when it allows for breakthroughs, it is very gratifying, I must say!