Now, I don't recall getting this book, and I assume that it came in with a bunch of other math/science books, being sort of about "Chaos", and this would have been a fairly likely purchase for me in the late '80s to early '90s. Frankly, it's a bit of an odd book ... it takes a look at biological systems from a mathematical standpoint, or roughly the title of chapter 2: "Steady States, Oscillations, and Chaos in Physiological Systems". The authors note that most researchers in the biological sciences are not particularly mathematically inclined (or trained) and point out that these systems, were they exhibiting these patterns in any other context, would be likely to have been long since subjected to "mathematical models subsumed under the rubric 'Theory of Dynamical Systems'". The authors attempt to fill this gap by "the applications of mathematics to the study of normal and pathological physiological rhythms".
One other thing to note about this book, it is pretty clearly intended as a textbook, and its target would seem to be upper-level undergraduates, and while they make a valiant effort to "buffer" the mathematics involved (shunting much of it off to a rather extensive, and somewhat hard-to-follow, appendix), there still is quite a lot of complex equations being thrown around, along with various charts and graphs to illustrate what's going on in the math. Oh, and if the sub-title "The Rhythms of Life" gets you humming tunes from The Lion King, this is a book that would get P.E.T.A. fuming as almost every "rhythm" measured involves probes stuck into cats, dogs, rats, etc., some alive (but paralyzed), some "in vitro". Even I got creeped out about this, and "animal rights" stuff almost never registers with me (one footnote did report on the possibility of a particular researcher dying from doing an experimental study on his own heart ... so there are some researchers who aren't cutting open Rover to see what makes him tick).
Well, at this point, I'm guessing 90-95% of folks looking at these pixels have already decided that they're not likely to want to check out From Clocks to Chaos, but not only is it obscure, difficult, and somewhat squicky ... it also has blocks of prose like this to contend with:
Aside from loving the phrase "attractor basin" (which is quite evocative for some chaos models), who's going to get something like that on the first read-through? It certainly doesn't help that the next paragraph launches into an equation with cos 2πφ' on the left side of the equals sign (never mind what's on the right, but it's not pretty) ... and much of the book goes like this!The locus of all points with the same latent phase is called an isochron. An isochron is a smooth curve (for limit cycles in two dimensions) crossing the trajectories in the attractor basin of the limit cycle. The state point on any trajectory in the attractor basin of the limit cycle passes through all the isochrons at uniform rate. Thus isochrons are very close together whenever time derivatives are small. In particular, isochrons come arbitrarily close together at any fixed point and therefore necessarily also along any singular trajectory leading to a fixed point. The locus of stationary states and attracting sets of these stationary states is called the phaseless set. Except for the phaseless set, one and only one isochron passes through each point in the attractor basin of the limit cycle.
Anyway, the other clue that this is a textbook is that it's still in print 20 years later, and that the cover price is a whopping $45.00 ... sure it has over 30 pages of references, but that's steep. If for some inexplicable reason all the above has whetted your appetite for just this sort of mental snack, it is available via the new/used vendors for as little as $4.27 (before shipping) for a "very good" copy. However, needless to say, this is one that we can chalk up to "Brendan needed a particular brain input" and not feel deprived that you haven't read it too!