Floquet Multipliers - Dynamical Systems | Lecture 29

Now that we've learned about Poincare mappings, we can use them to analyze the stability of periodic orbits. In this lecture we show that the stability of a closed orbit in continuous-time is equivalent to analyzing the linearization of the Poincare map about a fixed point. The eigenvalues of the linearization are called the Floquet multipliers of the periodic orbit and we show that if all of them lie inside the unit circle of the complex plane then the closed orbit is stable. We further demonstrate the theory with two worked examples of varying complexity.

Learn more about Floquet theory: https://en.wikipedia.org/wiki/Floquet...

This course is taught by Jason Bramburger for Concordia University.

More information on the instructor: https://hybrid.concordia.ca/jbrambur/

Follow @jbramburger7 on Twitter for updates.