By this point in the course, I hope you have the sense that most phenomena in nature are nonlinear, from the beating of a heart to the dynamics of the climate to fluid flow and much more. This unit exposes you to some of the fundamental ideas of analyzing nonlinear systems, which usually have no closed-form solution.
By the end of this lesson, you should be able to:
- Compute fixed points, null clines, and phase portraits of phase plane systems.
- Calculate stability of fixed points in nonlinear systems.
- Connect information about fixed points in nonlinear systems and information about those points in linearized systems.
Before class, please:
- Read Strogatz, Sections 6.0 - 6.4.
- Watch Introduction to 2-d Nonlinear Systems and Linearization of Nonlinear Problems.
- Check yourself before you wreck yourself.
In class, we will:
After class, please: