Indiana University Bloomington

Psychological and Brain Science Q580
Intro. To Dynamic Systems In Cognition

Contact: Jim Townsend (jtownsen@indiana.edu) date: 10/29/12
Capacity: 15
Sequence: NA
Pre-Requisites: Introductory differential equations helpful but not mandatory. Otherwise, see items 20-22.
Algebra Required: Linear algebra and matrix theory. Used for all three.
Calculus Required: At least two terms of differential and integral calculus. Also used for all three.
Contact Person for Authorization: Just grad. Status.
Instructor: J. Townsend and alternately, R. Beer.
Days Per Week Offered: 2 or 3.
Recommended follow-up classes: Advanced undergraduate or grad-level differential equations.
Syllabus: Download Syllabus
Keywords: Deterministic linear and nonlinear systems; catastrophe theory; chaos theory.
Description: My philosophy in this course is to give participants a solid introduction to dynamic systems. Given the massive size of the field and the limited time, we have to carefully select the topics to cover. Because I believe that the student cannot really comprehend nonlinear systems without a pretty thorough understanding of linear systems, that is where we start: first order, 1-dimensional, homogeneous, continuous time, linear systems. As the former indicates, we focus on continuous time systems. If one understands these, it is relatively easy to learn discrete time systems, but the converse is not so true.
Books: Boyce & De Prima, Differential Equations; Beltrami, Dynamic Systems; Devaney, Chaos Theory.
Substantive Orientation: Psychological and biological sciences. Applied and theoretical statistics and quantitative modeling. Computer science, especially HCI and AI.
Statistical Orientation: NA
How Software is Used: Programming and computation.
Problem Sets: Yes.
Data Analysis: Not usually.
Presentation: Not required by invited.
Exams: No.
Comments: A paper applying dynamic systems theory to a theoretical research problem of interest to the student.