This course provides an introduction to nonlinear dynamical phenomena, focusing on the behavior of systems described by ordinary differential equations.

Dynamical systems theory provides a framework for thinking about the behavior of models of real-world systems. Our focus in this course is on building intuition for this geometric way of thinking. To that end, we will study stability and bifurcations in depth. In addition, we will be exposed to the following topics: chaos; routes to chaos and universality; approximations by maps; strange attractors; fractals. Techniques for analyzing nonlinear systems are introduced with applications to physical, chemical, and biological systems such as forced oscillators, chaotic reactions, and population dynamics.

The methods and perspective that come with studying dynamical systems are of contemporary importance. The following text is taken from SIAM's introduction to a recent Applied Dynamical Systems conference: "The application of dynamical systems theory to areas outside of mathematics continues to be a vibrant, exciting and fruitful endeavor. These application areas are diverse and multidisciplinary, ranging over all areas of applied science and engineering, including biology, chemistry, physics, finance, and industrial applied mathematics. "