Limit Cycles: Existence and Non-existence Criteria
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Lesson Description:
Limit Cycles: Existence and Non-existence Criteria -- Lecture 32. Learn about limit cycles and their criteria.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
Additional Resources:
- Lecture Notes - Lecture Notes
- Linear Systems Notes 6 - Linear Systems Notes 6
Questions answered by this video:
- What are limit cycles?
- What are the criteria for limit cycles to exist?
- What is a closed trajectory?
- What does it mean for a limit cycle to be isolated?
- What does it mean for a limit cycle to be stable?
- How do you know when a limit cycle will not exist?
- What is Poincare-Bendixson criteria?
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Staff Review
This lecture starts off with a bit of review from the last few lectures, including trajectories and velocity fields. This lecture is devoted entirely to the idea of limit cycles and how to determine whether a limit cycle exists. There are some example problems done as well. A very interesting topic explained very well.
