Uploaded July 2017 | Updated September 2026, 2 weeks ago

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In this video (which happens to be my first ever 1080p video!), I discuss linear stability analysis, in which we consider small perturbations about the fixed point, and then analyze the local behavior of the differential equation/dynamical system around the fixed point.

The derivation involves a simple linear expansion of the differential equation function around the fixed point. When the x derivative of the ODE function f(x) is positive, we have an unstable fixed point. When it's negative, we have a stable fixed point. I didn't discuss a special (but more rare case) in the video, but when f'(xf) is zero, we usually have a 'half-stable' fixed point (stable from one direction, unstable from the other).

Questions/requests? Let me know in the comments below!

Prereqs: The first 2 videos in my Nonlinear Dynamics/Dynamical Systems playlist: youtube.com/playlist?list=PLdgVBOaXkb9C8iPDD5xW0jT-c3dtP4TR5

Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4UkZFbndqWWZMVHc/view?usp=sharing&resourcekey=0-CC2DbS1SQek-yrK_Ea4h3g
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Special thanks to my Patrons: Jacob Soares