Introduction to Dynamical Systems and Chaos (2022)
Lead instructor: David Feldman
 About the Course:
In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:
1. Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's behavior.
2. Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
3. Disordered behavior can be stable. Nonperiodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
4. Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
 About the Instructor(s):
The course creator and instructor, David Feldman is a Professor of Physics and Mathematics at College of the Atlantic. From 20042009 he was a faculty member in the Santa Fe Institute's Complex Systems Summer School in Beijing, China. He served as the school's codirector from 20062009. Dave is the author of Chaos and Fractals: An Elementary Introduction (Oxford University Press, 2012), a textbook on chaos and fractals for students with a background in high school algebra. Dave was a U.S. Fulbright Lecturer in Rwanda in 201112.
 Class Introduction:
 Class Introduction
 How to use Complexity Explorer:
 How to use Complexity Explorer
 Enrolled students:

863
 Course dates:

Always available
 Prerequisites:

A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.
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Syllabus
 Introduction I: Iterated Functions
 Introduction II: Differential Equations
 Chaos and the Butterfly Effect
 Bifurcations: Part I (Differential Equations)
 Bifurcations: Part II (Logistic Map)
 Universality
 Phase Space
 Strange Attractors
 Pattern Formation
 Summary and Conclusions