Imperfect Bifurcations - Dynamical Systems | Lecture 9

We saw in the previous video that symmetry plays a critical role in pitchfork bifurcations. But what about when that symmetry is broken? The result is a kind of imperfect bifurcation. In this lecture we study a specific example of an imperfect bifurcation, sometimes called a cusp bifurcation, and show what happens when the symmetry of a pitchfork is broken. The system under consideration has two parameters, one bifurcation parameter and one imperfection parameter, resulting in a significant jump in complexity from the previously studied 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.