1.1 Stability of Fixed Points PROOF | Nonlinear Dynamics

Part 1:    • 1.0 A better way to understand Differ...  
Part 2:    • 2.0 A better way to understand Differ...  
Part 3:    • 3.0 A better way to understand Differ...  

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
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