Self-organized Patterns in Biological Systems from Reaction-Diffusion Modelling viewpoints

Masayasu MIMURA

Department of Mathematical and Life Sciences
Institute for Nonlinear Sciences and Applied Mathematics
Graduate School of Science, Hiroshima University

Regular and irregular spatio-temporal patterns have been observed in biological and chemical systems so far. Among them, self-organized patterns have been described by reaction-diffusion (RD) systems. Numerical calculations reveal that RD systems generate a variety of complx patterns, even if the systems look so simple. The occurrence of such self-organized patterns arising in RD systems is originally stated by Turing who introduced the idea of ``difusion-induced instablity'' into the explanation of cell differentiation and morphogenesis in developmental biology. Since then, his idea have been found not only in biology but also in physics, chemistry, ecology and other scientific field. In my talk, I would like to discuss self-organized growth and aggregation in biological systems and explain how these can be modelled by RD systems and consider what kind of self-organized patterns are generated by using analytical and complementarily numerical methods. Especially, motivated by growth pattern of E. coli and aggregating pattern of slime mold, I would like to focus my talk on biological movement due to chemotaxis from pattern formation viewpoints.