Spring 2000 EXCSCI 797N
Nonlinear Dynamics of Human Movement

Instructors: R.E.A. Van Emmerik & M. Rosenstein

Dates: TUTH 11.15-12.30 (Totman, room 156)

Introduction

One of the most important scientific developments in the last two decades is the wide-scale emergence of nonlinear dynamics and chaos theories. Nonlinear dynamics is the field of study that is concerned with dynamical systems in the form of differential and difference equations and the diverse phenomena that occur in these systems (attractors, transients, bifurcations and chaos). This theory, which is first and foremost mathematical, but has many intersection points with physics and the sciences, has tremendous potential for handling fundamental problems in astronomy, meteorology, economy, biology, psychology, and medicine. In some areas, such as heart disease and brain functioning nonlinear dynamics and chaos theory have drastically changed our views of health and disease. The role of variability is crucial in this context. Whereas more traditional cybernetic models have emphasized the detrimental aspects of variability, the dynamical approaches have stressed the functional significance of variability in physiological signals. In movement control and coordination research, dynamical and complex systems perspectives are now powerful approaches that are beginning to yield new insights in patterns formation during development and disease.

Objectives

The present course focuses on concepts and principles from nonlinear dynamics, dynamical and complex systems approaches in order to gain an understanding of the significance of these approaches for movement coordination and perception. Topics to be discussed will be: basic concepts of nonlinear dynamics, the dynamical systems approach to movement coordination, oscillator theory, and exploiting dynamics.

 

Required Text:

Kelso, J.A.S. (1995). Dynamic patterns: the self-organization of brain and behavior. Cambridge, Massachusetts: MIT Press.

Recommended texts:

Stewart, I (1989). Does god play dice? The mathematics of chaos. New York: Basil Blackwell, Inc.

Strogatz, S.H. (1994). Nonlinear Dynamics and Chaos. With Applications to Physics, Biology, Chemistry, and Engineering. Reading, Massachusetts: Addison Wesley.

Structure of lectures:

The class will be a mixture of lecture and seminar. During the lecture the instructor will present the main concepts, followed by time for discussion and questions. The seminar part of the course will consist of joint discussion of selected papers.

Evaluation:
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