Dynamical systems appear as models in applications whenever a nontrivial mechanism is at work. Dynamical systems are an ever-evolving component of mathematics. The different contexts include physics, chemistry, biology, economics and also the social sciences.
In this course students will develop an understanding of the intriguing properties of dynamical systems. They will learn how to extract information from the model which is essential for the application of interest. Both discrete time and continuous time dynamical systems will be considered, leading to nonlinear (iterative) maps and (ordinary) differential equations.
Famous examples from population dynamics in biology will be studied. Mathematical existence and uniqueness results reflect the deterministic nature of the models. Students will study linear dynamical systems, stationary states and their (in)stability, periodic behavior, chaos, global behavior of scalar maps and differential equations in the plane, as well as bifurcation theory.
This course is part of both the Social Systems and Cities and Cultures themes, making it particularly well suited for cross-cutting analyses of these two major areas.
