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!

Electricity and Energy on America Revealed Tonight

Tonight's episode on the excellent PBS TV series America Revealed is, Electric Nation, and it will be broadcast ET at 10 PM.

I will be watching.

According to the description of tonight's episode:

Our modern electric power grid has been called the biggest and most complex machine in the world – delivering electricity over 200,000 miles of high tension transmission lines.  But even though the grid touches almost every aspect of our lives, it’s a system we know very little about.

My research group has done research on electric power network systems and also on network vulnerability from transportation systems to supply chains.


Episode 1 was on food and episode 2 was on transportation.

Next week it will be on manufacturing.


I wrote up  some of the  highlights of the transportation segment.

Building a Resilient World by Preparing for Disasters

Dr. Judith Rodin, the President of the Rockefeller Foundation,  has a wonderful OpEd piece on cnn.com, To Prepare for Disasters, Have a Plan B.

The article notes the meeting that is being convened in Washington DC this week, Embracing Change: Building Social, Economic, and Environmental Resilience.

To alleviate and reduce the impacts of food shortages, financial contagion, natural disasters, as well as pandemics, the world needs to harness the power of networks and synergistic collaborations.

This semester, I have been teaching a new course, Humanitarian Logistics and Healthcare. In the course, we have learned about emergency preparedness, mitigation, disaster response and recovery as well as risk management,  vulnerability assessment, the importance of critical infrastructure robustness and resilience. We have even discussed fund raising for humanitarian relief organizations.

Our guest speakers have come from the Red Cross,  the National Guard,  and from industry, and we have learned about Disaster Communications, and how universities prepare for emergencies.



As a public service, I have now made my lectures notes, as well as several guest speaker talks, available online.

This course was inspired by the Humanitarian Logistics: Networks for Africa Workshop that I organized at the Rockefeller Foundation's Bellagio Center on Lake Como, Italy.

The findings from the workshop as well as the presentations can be accessed here.

Thanks to the Rockefeller Foundation for sponsorship.

Our books on related topics can be found here.

America on the Move -- Transportation Episode on America Revealed Tonight

Having enjoyed the first episode of America Revealed last week, which was on food, I am looking forward to tonight's segment, "America on the Move," which will focus on transportation systems.


More information about tonight's show, with video clips, can be found here.

Last week, I was interviewed on this production for the PBS affiliate WGBY 57 TV show, Connecting Point.

You can view my interview in NYC with Yul Kwon, the host of America Revealed. In that interview I spoke on the Braess paradox and gridlock.

Nice to see network systems getting so much attention and generating so much interest!