South African Journal of Science
On-line version ISSN 1996-7489
Print version ISSN 0038-2353
BANASIAK, J.. Chaotic linear systems in mathematical biology. S. Afr. j. sci. [online]. 2008, vol.104, n.5-6, pp.173-179. ISSN 1996-7489.
Chaotic phenomena occurring in the natural sciences have been a focus of interest of both theoreticians and experimentalists for over five decades. Usually associated with nonlinear systems, they can also appear in infinite dimensional linear ones; that is, governed by, for instance, infinite systems of ordinary differential equations or partial differential equations. In this paper we shall provide a survey of mathematical tools which are necessary to analyse chaotic linear systems and discuss several examples of such systems arising in mathematical biosciences, ranging from drift-diffusion processes, through mutations, to the production of blood cells. We shall also attempt to address some questions related to the relevance of the mathematical analysis to properties of real-life systems.