summarizing their recent work on the control or epithelial 

 morphogenesis in cultured salivary glands, and the role therein 

 of surface-associated mucopolysaccharide-protein complexes and 

 microfilaments. f-l<^aco aim 



In a brief 



gaps between 



& J- -w.,^ wj, wd^ ui ci speculative 



theoretical model. 



The book is well produced and illustrated. 



introductory chapter Runner tries to bridge the 

 the various contributions by way of a speculati^ 



THEORETICAL DEVELOPMENTAL BIOLOGY (see also 5) 

 Monographs 



7. 



R.ROSEN. 1970. DYNAMICAL SYSTEM THEORY IN BIOLOGY. 

 Vol.1. Stability theory and its applications 



Wiley-Interscience, New York, etc. XIV, 302 pp., 86 figs., com- 

 bined author and subject index. $ 17.95, £ 8.50 



Systems of differential equations have been widely used in Di- 

 ology, but as the experimental situation is usually more complex 

 than in the non-biological areas of application, any mathematical 

 model-building becomes an uncertain affair. Therefore, the study 

 of the stability properties of such systems (What are the effects 

 of small changes in the initial conditions? Does the system reach 

 a stable state? What are the effects of structural changes in the 

 system?) is of particular importance for biological applications; 

 stability theory concentrates on the kind of behaviour exhibited 

 by dynamical systems rather than on quantitative results. 



In the first six chapters the author presents a treatment of 

 stability theory with an eye on Diological applications. The Dook 

 is intended for "... those with only a first course in calculus, 

 or who are not sure what a matrix is", with suppression of the 

 finer mathematical points and emphasis on geometric intuition. 

 Indeed, the account is readaole enough without being sloppy (al- 

 though there are a number of mistakes). 



The last three chapters deal with more strictly biological mat- 

 ters. The notion of a dynamical "metaphor" (weaker than a model"" 

 is introduced. Subjects treated in these chapters are: the Ras- 

 hevsky-Turing construction, Goodwin's theory, reaction kinetics 

 and katalysls, excltation-inhlDition systems, and networks built 

 from such systems. The last chapter first explains the formalism 

 of statistical mechanics and then proceeds to discuss Volterra 

 systems and Goodwin networks. 



It is perhaps unfortunate that the author chooses to stay safe- 

 ly on the mathematical side of his problems, hardly ever ventur- 

 ing into biology proper. Even the biological chapters deal with 

 metaphors rather than models and cannot claim to be much more 

 than biologically inspired mathematics, with most of the oiology 

 being in the footnotes. As a result, the reader, though feeling 

 conceptually enriched, is left with the helpless feeling of 

 having a powerful tool and not yet knowing what to use it on. 



Still, the book gives a clear presentation of an important 

 field. It is based on lecture notes for graduate students in 

 mathematical oiology, and contains a fairly large number of ex- 

 ercises. Volume II will deal with control systems, input-output 

 analysis, and optimality. 



P.G.Doucet, Centr. Interfac. for Philosophy, Univ. of Utrecht 



13 



