The Coolness of Dynamical Systems and Equilibrium Analysis -- from Economics to Ecological Systems to Even Sleep!

I work on systems and have beem fascinated by systems, especially network systems, since I was a child.

Who does not love transportation, for example -- from riding busses and trains, to flying, to trying out a motorcycle or a convertible?

I am especially intrigued by how actions of many individuals affect the outcomes in systems and have worked on large-scale transportation network models, food supply chains, and even ecological predator-prey networks.

I use such methodologies as network theory, optimization theory, multicriteria decision-making, game theory, as well as variational inequality theory and projected dynamical systems theory (which I helped to develop). in my research. The applications that I focus on are often of interest to many disciplines from operations research and management science to economics and engineering.

In studying complex systems,  equilibrium analysis may be interpreted as a generalization of optimization theory. Essential to such analysis is also capturing and understanding the underlying dynamics since deicison-makers interact over space and time.

Steven Strogatz's piece in The New York Times  is so beautifully written that it deserves mention and I will digress from finishing up a paper, for this reason.

I am seated in my lovely office at the School of Business, Economics and Law at the University of Gothenburg, in Sweden, where I am spending part of my sabbatical and I have been writing about my wonderful experiences here.

Strogatz, in his essay, not only points out the importance of equilibrium analysis in many different systems from the ones that are more apparent, such as those in economics, and in ecology, but also regarding sleep.

In his beautifully written piece, he captures the elegance of mathematics and how it can explain important phenomena and focuses on catastrophe theory!

When mathematics combines with fascinating applications and great writing we can say that man has evolved to a level that we should be celebrating!

Do the math or, at least, appreciate it and its powers,  and continue to see the wonders in our world!