Q580 | 25243 | R. Beer

Q580 , 25243 , Beer TuTh, 1:00-2:15pm, Room: TBA Introduction to Dynamical Systems in Cognitive Science Q580 Randall Beer Concepts from dynamical systems theory are becoming increasingly important in cognitive science, and the construction and evaluation of dynamical models requires a thorough understanding of the mathematical theory of dynamical systems in the same way that computational models in cognitive science require a thorough understanding of computation. This course provides such an introduction to dynamical systems theory, with an emphasis on the underlying mathematical ideas and tools. Although we will focus on dynamical systems formed by sets of differential equations, we will also cover discrete- time dynamical systems at several key points. The course will begin with a comprehensive study of one and two-dimensional systems and then proceed to the general case. At each step, we will examine the limit sets, stabilities, phase portraits and bifurcations that are characteristic of that dimension. Throughout the course, applications drawn from a wide variety of areas will be used to illustrate the mathematics. We will also make heavy use of computer tools for analysis and visualization.