In this lecture we introduce the concept of a gradient system. In particular, we show that if a dynamical system has a gradient structure then it cannot have any closed orbits. The result of a gradient structure is that, much like the case of one dimensional flows, we can interpret trajectories as flowing downhill on a potential landscape. Gradient systems are special in that their behaviour is relatively simple - one can only evolve to a fixed point, much like in one dimension.
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.
