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One-Dimensional Mappings - Dynamical Systems | Lecture 30

We motivated the study of discrete-time mappings with the Poincare map, so now let's see just how complicated they can get. In this lecture we are introduced to the basics of one-dimensional mappings, including fixed points, their stability, cobweb diagrams, and cycles. We present a number of examples, including a long worked example on the logistic map. We see that we can again get bifurcations (saddle-node, transcritical, pitchfork) in these mappings, but now we are introduced to another new one: the period-doubling bifurcation. We show that the logistic map undergoes a series of period-doubling bifurcations eventually culminating in chaos. 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.