Introduction to the geometric / graphical approach for analyzing nonlinear ordinary differential equations, including fixed points and their stability. Next, an example: population growth model https://youtu.be/iOumaIR5gzA
► Dr. Shane Ross, Virginia Tech professor (Caltech PhD)
Ross Dynamics Lab: http://chaotician.com
► Next: Population growth model (logistic model)
https://youtu.be/iOumaIR5gzA
► See also 2D and 3D dynamical systems
2D https://youtu.be/oNij9lns5RI
3D https://youtu.be/fIG2jtOhW0U
► Related videos
Example of over-damped bead in a rotating hoop https://youtu.be/UOQxFf1eSJs
Flows on the circle https://youtu.be/Q_0oB1DHyQU
Flows in 2D https://youtu.be/oNij9lns5RI
Linearization near fixed points in 2D https://youtu.be/m0d3sLqPftA
► From 'Nonlinear Dynamics and Chaos' (online course).
Online course playlist https://is.gd/NonlinearDynamics
► New topics posted regularly.
Subscribe https://is.gd/RossLabSubscribe
► Course lecture notes (PDF)
https://is.gd/NonlinearDynamicsNotes
Reference: Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 2: Flows on the Line
1D vector field autonomous time-independent nonlinear dynamics dynamical systems differential equations dimensions phase space Poincare Strogatz graphical method Fixed Points Equilibrium Equilibria Stability Stable Point Unstable Point Linear Stability Analysis Vector Field One-Dimensional 1-dimensional Functions
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