Turing theory plays an important role in real biological pattern formation problems, such as solid tumor growth and animal coat patterns. To understand how patterns form and develop over time due to growth, we consider spatiotemporal patterns, in particular Turing patterns, for reaction diffusion systems on growing surfaces with curvature. Of particular interest is isotropic growth of the sphere, where growth of the domain occurs in the same proportion in all directions. Applying a modified linear stability analysis and a separation of timescales argument, we derive the necessary and sufficient conditions for a diffusion driven instability of the steady state and for the emergence of spatial patterns. Finally, we explore these results using numerical simulations.

微生物から人類まで、地球上のすべての生命体は、非平衡開放条件下で生命活動を維持している。生物が織りなすさまざまな生命現象の基礎となり、生物を生物たらしめている本質的なものは、非平衡開放条件下での「自己組織化現象」や 「時間発展的な自己秩序化現象」と言える。本論文は、生命体そのものではなく、その自己組織や自己秩序化についての実空間の簡単なモデル系を取り上げて、研究を行った結果をまとめたものである。 / From microorganisms to human beings, all living organisms on the earth maintain life activities under non-equilibrium open conditions. "Self-organizing phenomena" or "time-evolving self-ordering phenomena" under non-equilibrium open conditions are essential things that serve as the foundation of various life phenomena woven by living things and that keep living things as creatures. By taking a simple model system of real space about its self-organization and self-ordering, this paper summarized the results of research processed. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University