拡散が作り出す時空間パターン(<特集>パターンダイナミクス)

抄録

In 1952, Turing showed that diffusion does possibly enhance spatial inhomogeneities in some situation, by using simple reaction-diffusion equations. This paradoxical argument demonstrates that diffusion generates spatio-temporal patterns, which is mathematically supported by the stability theory of differential equations. In many biological, chemical and physical systems, we have encountered a variety of diffsuion-induced spatiotemporal patterns suggested by Turing. In this note, among these patterns, we concentrate ourselves on bacterial colony patterns arising in biological systems. We discuss on the diversity of colony patterns observed in experiments, by using a reaction diffusion equation model which is proposed on the idea of Turing's paradoxical argument. Furthermore, we apply this idea to understanding of spatio-temporal patterns arising in more general consumer-resource systems. As an example, we discuss combustion in micro-gravity circumstance from pattern formation viewpoints.