The understanding of complex systems is itself a complex
process: It is too easy to detect patterns at one level
(especially if the patterns are represented with esthetically
stimulating graphics) and then to generalize what one has learned
to assume that this pattern applies to the rest of complex systems
as well. Mike Shlesinger, a veteran of chaos theory himself,
apparently liked the pictures that you can produce with coupled
map models so that he assumed that the book was about
spatio-temporal chaos. This restricted (and admittedly not so
biologically relevant) class of models is discussed in chapter 3
of the book. He somehow missed that the more important message of
the book was not a recipe to produce pretty pictures but to offer
a serious contribution to a computational approach to complex
systems with a special focus on biological networks including the
brain.
The general class of models that the authors propose (GCM =
"globally coupled maps") is general enough to allow accurate
implementation of, say, brain models with any desired degree of
realism. One can appreciate how powerful GCM's are by recognizing
that they also include network models of the "Small World"
category that have been widely discussed recently. As a contrast,
cellular automata or coupled map models do not share this
property.
In terms of modeling strategy we are convinced that this book
will have a fundamental impact on the new, systems-oriented
biology. Demonstrating how one can build mathematical models with
the ideas of mapping states into each other as they evolve in time
can have tremendous heuristic values and frees theoretical
bio-scientists from squeezing their creative ideas into the
language of stocks, flows and rates. This discrete time approach
also encourages the modeler to carefully analyze the relevant
time-scales that are relevant in the modeled system.
Excerpt: Kaneko and Tsuda also seek ways of measuring the
complexity of their systems. They define an information flow and
entropy derived from the number and size of synchronized spatial
clusters. And they make analogies between information storage,
flow and processing in the brain and the many possible states of
the coupled map lattice (…). Spatiotemporal dynamics of
nonlinear coupled map lattices is a new field of study, and much
remains to be done to determine whether it will be a fruitful
approach to biological problems.