โ Scribed by G. Bard Ermentrout
No coin nor oath required. For personal study only.
Dynamic Patterns: The Self-Organization of Brain and Behavior by J. A. Scott Kelso represents a summary of the research and philosophy driving the work of Kelso and his collaborators over the last several years. A closely related book that I will also review is Principles of Bruin Function by Hermann Haken. The relationship between these two books is that Kelso has extensively collaborated with Haken and thus Haken's synergetics is the main theoretical tool used in both of these books. Kelso's book is the better of the two in the sense that there is a big picture drawn, whereas Haken's book consists mainly of examples. I suppose, as an outsider, Kelso is able to explain synergetics to the reader in a much clearer fashion. Synergetics, while never actually defined, is essentially an attempt to reduce complex interacting systems to a few nonlinear differential equations. When applied to a specific model, it is essentially an application of Liapunov-Schmidt or normal form methods with the addition of noise. Basically, the idea is to take very complex phenomena such as locomotor gaits or behavioral switching and reduce the dynamics to a set of low-dimensional differential equations in terms of the so-called order parameters. Often this is done in an ad hoc manner; that is, the equations that are written are meant to be descriptive and are not often derived from some underlying physical principles. For example, Kelso has devised a clever set of experiments in which subjects are asked to tap their right and left fingers at a rate prescribed by a metronome. There are two basic patterns: in-phase and anti-phase. The subjects were instructed that if they felt the phase pattern begin to change they were not to consciously prevent it from changing. What Kelso finds is that at low frequencies, the subjects can produce in-phase and anti-phase tapping, but at higher frequencies only in-phase is possible. Given that phase is the relevant variable and that the two fingers are symmetric, Kelso, along with Haken, devised a simple model 4 for the phase difference between the two fingers: d4 dt---asin 4-2bsin24.
๐ SIMILAR VOLUMES