Introducing Bifurcations: The Saddle Node Bifurcation

Welcome to a new section of Nonlinear Dynamics: Bifurcations! Bifurcations are points where a dynamical system (e.g. differential equation) undergoes a significant change in its dynamical behaviour when a certain parameter in the differential equation crosses a critical value. In this video, I explain saddle node bifurcations. These are bifurcations in which varying a parameter causes the appearance of a half-stable fixed point, followed by two fixed points from nothing. I discuss bifurcation diagrams, bifurcation points, and describe the concept of normal forms. Questions/requests? Let me know in the comments! 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=1mt_5XJqUB6wtST-J0KBlRhSJY5v7lM7q Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan Special thanks to my Patrons for supporting me at the $5 level or higher: - Jose Lockhart - James Mark Wilson - Yuan Gao - Marcin Maciejewski - Sabre - Jacob Soares - Yenyo Pal - Lisa Bouchard - Bernardo Marques - Connor Mooneyhan - Richard McNair