AM 108 S17 Nonlinear Dynamical Systems

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

Dynamical systems theory provides a framework for thinking about the time evolution 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, the course will touch on 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.

Dynamical systems theory is an area of mathematics that has found a number of applications. Searching Google Books for "dynamical systems" yields results such as "Dynamical Systems and Their Applications in Biology", "Dynamical Systems in Cosmology", and "Dynamical Systems in Neuroscience" as well as a number of books that add noise to dynamical systems or are oriented towards control of a system. Talks at SIAM's 2015 Applied Dynamical Systems conference included ones on extreme events, on cancer, on energy transfer, on climate, on fluids, on the brain, and on dynamical systems on networks.

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Sarah Iams