Dynamical Systems Analysis

This course intends to give the student a practical working understanding of some of the techniques for analysis of dynamical systems. Both theoretical ideas and practical applications will be covered, with special emphasis given to those techniques which are robust in the presence of chaotic dynamics. The course will begin with an overview of the concepts and theory behind dynamical systems. A variety of examples of dynamical systems from Developmental, Social, Cognitive, Neuroscience and Clinical Psychology will be presented in order to give the student some perspective on when Dynamical Systems techniques might be useful. During the second portion of the course we will develop handson familiarity with some different types of dynamical systems by using software (Maple and STELLA) that simulates different dynamical systems and plots their behavior. We will use this software to gain an intuitive understanding of different types of attractors and repellors that might occur in Psychological data. The third portion of the class will cover some techniques for time series analysis. We will learn how to create time series plots, recurrence diagrams and phase space plots. We will learn about Fourier transforms and how to read a Fourier periodogram plot. We will end the time series section with a discussion of stationarity and ergodicity, two concepts important when creating models of time series. During the time series portion of the class, we will learn to use a program called Splus. This is a Windows and Unix program that makes it easy to perform many of the common time series analysis functions. Next, some practical methods for determining optimal sampling lag, embedding dimension, fractal dimension and nonlinear dependency from a sampled time series will be presented. During this portion of the course, the students will use programs written by the instructor which can perform these calculations on the student's own data. The remainder of the course will be devoted to the analysis of real world problems and the development and testing of dynamical systems models for behavior. Computer work associated with the course will involve working with R, Mathematica, and OpenMx as well as some new programs. Computer work will be used to develop an intuitive understanding of some simple dynamical systems. Students will also learn to use computer software to perform a dynamical systems analysis on real psychological data sets.

R and Mx Homework Files.

Nonlinear Dynamics Homework Files.

Steven M. Boker Department of Psychology University of Virginia Gilmer Hall Room 102 Charlottesville, VA 22903 Office: 4342437275, FAX: 4349824766 email: boker@virginia.edu 