Introduction to Dynamical Systems and Chaos
All-Time Top 100Santa Fe Institute via Complexity Explorer
- Provider Complexity Explorer
- Cost Free Online Course
- Session Self Paced
- Language English
- Certificate Certificate Available
- Effort 3-6 hours a week
- Duration 10 weeks long
- Learn more about MOOCs
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Overview
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. 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.
Taught by
Class Central Charts
- #2 in Subjects / Mathematics
- #1 in Subjects / Mathematics / Calculus
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Reviews for Complexity Explorer's Introduction to Dynamical Systems and Chaos Based on 105 reviews
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this review helpful
If you've done a bit of computer science or programming, this class shows a very interesting result from the simple idea of iteration.
The professor is interesting and makes the material intuitive. Regardless of your level of mathematical comfortability, this class is well paced and provides all the tools you need to proceed through it.
Don't miss this class!!
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Quite the opposite. The lead instructor David Feldman is always able to make even the more complex parts of this mooc easy to understand.
David has also developed a well featured web software for visualizing all the course material: equation orbits, Butterfly Effect, bifurcation diagrams and Strange Attractors patterns.
If you're a programmer, you can complete some of the advanced (but optional) exercises using the language of your choice. Here's my version in Python:
https://github.com/madrisan/dynamic-systems-and-chaos
In short this mooc has been a wonderful mathematical trip.
My deepest thanks to Professor Feldman. He is an extraordinary educator. He communicates clearly and makes the complex understandable. Despite his vast knowledge and expertise, he is still excited about the material he is teaching. Some of my favorite moments were his asides to make sure we appreciated how abstract concepts can be observed in physical systems. The course was well organized and I appreciated that all of the material was accessible for review and replay. The unit summaries were very helpful. I just sorry the course is over.
Next, the course itself is riveting not just because of the digestibility of the content, courtesy of the instructor, but also the availability of programs to engage and interact with that enforces the lessons that David provides.
David is also an engaging instructor and is able to deliver content at a pace and clarity that is oh so important for MOOCs. This is critical in understanding the key lessons or ideas or concepts he wants you to leave with at the tail-end of the course.
And of course, lastly, the subject itself is fascinating and absorbing once you start thinking about the real-world comparisons that David introduces quickly.
Only great professors uses scissors, pencils and papers and explain very complicated things with ease .
This course is a very good one, professor Feldman's explanations are really clears and complex materials "flows" very well .
Personally have already recommended this course to others and think that I will gladly follow other courses in which professor Feldman will be the teacher considering his high scientific level and his predisposition to teach in a simple way ( where he can ) ...
Simply great !!!
I am a math dummy and my background is mostly biology. This class did a so good job in explaining dynamical systems that I realized biological systems are likely to be ( maybe complex) dynamical systems. However, due to experimental limitations, molecular and cellular biologists hardly can study their systems as a dynamical system. After taking this class, I am decided to try to study biological systems (nervous systems, more specifically) as dynamical systems for my future work.
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