Introduction to Dynamical Systems and Chaos (Complexity Explorer)

Introduction to Dynamical Systems and Chaos (Complexity Explorer)
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A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.
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Introduction to Dynamical Systems and Chaos (Complexity Explorer)
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.

MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

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. Non-periodic 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.



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MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Free Course
A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.

MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.