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Stability and Local Linearization - Math Modelling | Lecture 17

Now that we have some familiarity with linear systems, we are going to leverage that knowledge to understand nonlinear equations. In particular, we show that we can produce linear systems near steady-states that can be used to determine the dynamics of the system in a neighbourhood of that equilibrium. If all the eigenvalues of the linearization have negative real part, then we can conclude that the steady-state is stable. This stability also provides a robustness of the system, which can further be used to study sensitivity. We demonstrate all of these aspects of the problem in this video, focusing on the hardwood-softwood example from Lecture 10 of this series. 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.