Complex Systems in Neurobiology Language and Speech

Sp&Hrg 803
Complex Systems in Neurobiology, Language, and Speech

Day 9
2 April 1998
More Dynamics of Complex Systems

Homework Assigned for Next Time
Readings Assigned for Next Time

Summary of this Day's Class
Additional Information
Readings Discussed in Class
Students Comments on the Readings

Homework Assignment 9 - Due 23 April 98
Last week we read:

Zeeman, E.C. 1976. Catastrophe theory, Scientific American, 4:65-83.

Zeeman, E.C. A catastrophe machine, Appendix in "Towards a Theoretical Biology Vol. 4", Ed. C.H. Waddington, International Union of Biological Sciences and Edinburgh University Press, Edinburgh, pp. 276-282.

For your homework, I would like you to construct a Catastrophe Machine. First play with the machine to get a feel for how it works and keep in mind the geometric structure of the stable positions (angle) of the disk and the positions a and b in the plane. Make a plot of the positions of point c where the disk undergoes a jump. This plot should end up looking like the figure in Figure 2.

Reading Assignment 9 - Read the articles by 23 April 98
Have emailed comments by NOON Wednesday 22 April 98

Kelso, J.A. Scott. 1995. How nature handles complexity, Chapter 1 in: Dynamic patterns. The self-organization of brain and behavior. MIT Press, Cambridge MA, pp. 1-28.

Kelso, J.A. Scott. 1995. Self-organization of behavior: The basic picture, Chapter 2 in: Dynamic patterns. The self-organization of brain and behavior. MIT Press, Cambridge MA, pp. 29-67.

Abraham, Ralph H. and Shaw, Christopher D. 1992. Part of: Chaotic Behavior, Sections 8.3-8.4 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 283-294.

Abraham, Ralph H. and Shaw, Christopher D. 1992. Attributes of Chaos, Chapter 9 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 295-329.

If you have time you can look these over again:

Abraham, Ralph H. and Shaw, Christopher D. 1992. Basic concepts of dynamics, Chapter 1 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 13-51.

Abraham, Ralph H. and Shaw, Christopher D. 1992. Classical applications, Chapter 2 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 53-85.