In this lecture we discuss fixed points of dynamical systems on the line. Fixed points go by many different names depending on the discipline, including steady-states, equilibria, and rest-states, all meaning the same thing. We introduce the basics of fixed points and discuss what it means for them to be stable. We analyze stability using the geometric perspective from the previous lecture as well as provide an analytic criterion for determining stability. We conclude the lecture by discussing what happens when the criterion is indeterminant.
This course is taught by Jason Bramburger for Concordia University.
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