학술논문

A mathematical model for pattern formation in biological systems.
Document Type
Journal
Author
Catalano, G. AMS Author Profile; Eilbeck, J. C. AMS Author Profile; Monroy, A. AMS Author Profile; Parisi, E. AMS Author Profile
Source
Physica D. Nonlinear Phenomena (Phys. D) (19810101), 3, no.~3, 439-456. ISSN: 0167-2789 (print).eISSN: 1872-8022.
Subject
80 Classical thermodynamics, heat transfer -- 80A Thermodynamics and heat transfer
  80A20 Heat and mass transfer, heat flow
Language
English
Abstract
A pair of rection-diffusion equations are studied by analytical and numerical methods, and the results are compared qualitatively to several embryological problems. Analytical results consist of straightforward linear stability analysis of the characteristic solutions of the linearized equations. Numerical solutions, obtained by the ``hopscotch'' method, are presented which show, among other things, that there are no simple rules relating the symmetry of the final solution to that of the initial perturbation. The computed solutions are compared, metaphorically, with compartmentation in {\it Drosophila\/} imaginal discs, development of tunicate eggs, and waves of cell division in early sea urchin embryos.