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Mathematical biology. Vol. 2: Spatial models and biomedical applications. 3rd revised ed. (English) Zbl 1006.92002

Interdisciplinary Applied Mathematics. 18. New York, NY: Springer. xxv, 811 p. (2003).
In this second volume, for Vol. 1 see the preceding review, Zbl 1006.92001, one starts with the last chapters of the first edition but the development towards specific biological configurations and towards a mechanism for understanding morphogenesis represents an important portion of the work. The main mathematical tools are partial differential equations (PDEs).
One looks at animal coat patterns and their formation (the furs of mammalians, the wings of butterflies, pigmentation on snakes). This is related to chemotaxis and modelled by PDEs. Bacterial patterns are studied too in the same spirit.
The author hypothesises that a mechanism for morphogenesis should include in a crucial way nonlinearity, coupling and stability (so that nearby patterns are identified as a stable equilibrium). Note that the work of R. Thom on this topic is not cited in the extensive bibliography (761 entries). Moreover, the couplings of the author should increase robustness but he does not mention feedback in this situation which is robustifying and which arises from interacting building blocks of systems.
Other chapters deal with attractive topics: wound healing (epidermal, dermal), regulation of brain tumours, neural models for pattern formation, control of epidemics, wolf territoriality.
There is an extensive index at the end. This set of volumes is very interesting and strongly recommended.

MSC:

92B05 General biology and biomathematics
92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology
92C15 Developmental biology, pattern formation
92C17 Cell movement (chemotaxis, etc.)

Citations:

Zbl 1006.92001
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