Module 8: Limit Cycles

Lectures and Related Content

Folder description

Please click the folder link above to access the Module 8 instructional content. Module 8 contains the following:

  • 08A: Introduction and Example
  • 08B: Ruling Out a Closed Orbit
  • 08C: Establishing a Closed Orbit
  • 08D: Example: the Liénard System
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Module at a Glance

Cell description

In this module we'll analyze isolated, closed limit cycle trajectories.

Objectives

  • Distinguish the dynamics of stable, unstable, and half-stable limit cycles.
  • Interpret the possibility of a closed orbit.
  • Test the existence of closed orbits.
  • Follow along with the development of a model for the love story in Gone with the Wind.

How to complete this module:

  1. Watch the video lectures 8A through 8F. 
  2. Complete the reading assignment.
  3. Respond to the discussion board question.
  4. Complete the quiz.
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Readings

Cell description

This week's reading assignment includes the following:

  • Strogatz, Steven H. Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, 2018. 
    • Chapter 7 (pp. 198-213)
  • Rinaldi, Sergio; Della Rossa, Fabio; and Landi, Pietro. (2013 Aug). A Mathematical Model of “Gone with the Wind.” Physica A: Statistical Mechanics and its Applications, Science Direct website. (Vol 392, Issue 15, PP. 3231 – 3239). Retrieved from: https://www.sciencedirect.com/science/article/pii/S0378437113002677?via%3Dihub

Rinaldi reading available through EReserves by selecting the Readings link above or from the left menu bar.  

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Module 8 Discussion

Cell description
  • Based on your reading of “A Mathematical Model of Gone with the Wind,” work through problem 7.2.19 from the Stogatz textbook, as a class, using this discussion forum.
  • Ensure the model is discussed and parts a-d of 7.2.19 are sufficiently answered. 

You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.

Due: Sunday 11:59 pm

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