Complexity Explorer Santa Fe Institute

Course Syllabus

Complexity and Dynamical Systems, Shaheen

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.

University of Colorado at Boulder
Sean Shaheen
Fractals, Cellular Automata, Agent-Based Modeling, Emergence, Complex Systems, Nonlinear Dynamics