Stochastic Cellular Systems

This book covers the basic and applied mathematics of locally interacting highly nonlinear multicomponent systems which have biological and technological applications including neural networks. It shows the behaviour which such systems can display and investigates both their abstract aspect and their applications to the problems of morphogenesis, neuronal activity and the theory of queues. Numerical and simulation results are appended wherever possible to the analyses. The subject lies at the intersection of many disciplines including mathematical physiology, statistical physics and deterministic cellular automata. Therefore, besides the cited applications, the theory is also of great relevance to the modelling of other biological, chemical, physical and socio-economic systems such as plant competition, genetics, enzymology and election voting. The book reviews the mathematical background and main results of the Russian school of investigators and broadens the co-operation between pure and applied mathematicians within biology, making it relevant to researchers working on nonlinear studies within both mathematics and science departments.