Part 1: https://youtu.be/ySfs8YVMY7Q
Part 2: https://youtu.be/I9UEBRya4X0
Part 3: https://youtu.be/6mLCFyEv3Z0
This video deals with nonlinear differential equations in the form:
dx/dt = f(x)
To find out whether a fixed point is stable or not, a linear stability analysis is done whereby the function is approximated as a line. If the slope of that line is positive then the fixed point is unstable. If the slope of that line is negative then the fixed point is stable.
Chapters:
0:00 Intro & Background
0:49 Taylor Series about Fixed Point
1:57 Solve Linearized Differential Equation
3:02 Stability from f'(x*)
4:54 Summary
5:35 Outro
Music:
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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