Complexity and Dynamical Systems
Fall Semester 2014
Instructor: Sean Shaheen
Office: ECOT 435
Lecture times: M, W, F 2:00-2:50 pm
Lecture room: M, F EE 1B55C (Main office conference room)
W EE 1B45 (OCS conference room)
Textbook: Dynamics of Complex Systems, Yaneer Bar-Yam, Westview Press, 1997.
Dynamics: The Geometry of Behavior, Abraham and Shaw, Addison-Wesley, 1992.
Chaos in Dynamical Systems, Edward Ott, Cambridge University Press, 2002.
Books (more of the popular-science variety)
Complexity: A Guided Tour, Melanie Mitchell, Oxford University Press, 2009.
The Computational Beauty of Nature, Gary William Flake, MIT Press, 1998.
The Self-Made Tapestry, Philip Ball, Oxford University Press, 1999.
Hidden Order, John Holland, Perseus Books, 1995.
Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, Manfred Schroeder, W.H. Freeman and Company, 1991.
Super Cooperators, Martin Nowak, Free Press, 2011.
The science of complexity - understanding how individual components of a system act collectively to reveal emergent behavior - has been a growing theme in physics, biology, chemistry, mathematics, ecology, and even fields such as economics over the last several decades. For instance, recently these ideas have been brought to bear on the global topic of sustainability (see SFI talk by Dr. Geoffrey West). In this course, we will cover the basic concepts and mathematical treatment of complex dynamical systems and will implement these into simple computer simulations. We will then apply these principles to address from a fundamental standpoint questions such as: Under what regimes of system behavior does complexity (and chaos and fractal structures, etc) arise? What makes a complex system inherently stable over the long run? What attributes of natural and human-engineered systems make them able to best adapt to changing environments? How can collections of agents act collectively to best facilitation adaptation? These principles will be discussed in the context of global concerns of complexity and nonlinearities in systems engineering, ecology, environment, energy, climate, and economy.
Course objectives and activities
List of topics
Grading will be broken down into the following contributions:
In-class problems and presentations 20%
Mid-term project (written + oral) 25% Oral presentation date: October 10, written report due October 13, 2:00 pm
Final project (written + oral) 30% Oral presentation date: December 12, written report due December 15, 2:00 pm