Potentials and Impossibility of Oscillations | Nonlinear Dynamics

After a long hiatus from this Nonlinear Dynamics, I have finally returned with a 4th video! In this lesson, I begin with proving that oscillations for a 1-D autonomous dynamical system of the form dx/dt = f(x) are IMPOSSIBLE.

Then, I introduce the concept of potentials of differential equations. Potentials are another useful way of examining a differential equation and are convenient quantities because they behave in a manner similar to potential energies in Physics (i.e. physical systems prefer a state of lower potential energy, similar to how dynamical systems here tend to lower their potential over time).

After introducing potentials, I finish off by solving a quick example problem which shows how potentials can be utilized to ascertain the behaviour of a nonlinear ODE.

Questions/comments? Let me know below!

Pre-reqs: The videos before this one on this playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9C8iPDD5xW0jT-c3dtP4TR5

Lecture Notes: https://drive.google.com/open?id=1Uyr2UB5hugKQaBi7JAlyFYvGj_KIww2O
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Видео Potentials and Impossibility of Oscillations | Nonlinear Dynamics канала Faculty of Khan