Transcritical Bifurcations - Dynamical Systems | Lecture 7

This lecture continuous our discussion of bifurcations in one-dimensional dynamical systems. Here we turn our focus to transcritical bifurcations. These bifurcations are characterized by two fixed points colliding and exchanging stability. Unlike saddle-node bifurcations, no fixed points are created or destroyed over the course of the bifurcation. We examine the normal form of the bifurcation and some examples. The last example is used to perform the variable transformation to put the Taylor expansion into the normal form, exemplifying its universality for transcritical bifurcations. This course is taught by Jason Bramburger for Concordia University. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.