On solutions of spatial pattern formation in nonlinear reaction-diffusion systems

1995 Fiscal Year Final Research Report Summary

• Project/Area Number: 06640339
• Research Category: Grant-in-Aid for General Scientific Research (C)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Doshisha University
• Principal Investigator: KAWASAKI Kohkichi Doshisha University, Faculty of Engineering, Professor, 工学部, 教授 (10150799)
• Project Period (FY): 1994 – 1995
• Keywords: Reaction-diffusion equation / Nonlinear equation / traveling wave / Spatial pattern / Chemotaxis / Dense-braching morphology

Research Abstract

Many organisms display chemotactic aggregation in response to the concentration gradient of attractant molecules to form variety of spatial patterns. As typically seen in bacterial colonies, cellular slim molds and swarming insects, it has been known that bacterial colonies could show very complex spatial pattern depending on various culture conditions such as nutrient concentration and the solidity of agar plate. In this study I have attemped to elucidate the mechanism of such pattern formation in bacterial colony by means of mathematical modeling. The chemotactic movement of bacteria were formulated by a nonlinear partial differential equation. Its numerical solution reproduces concentric spotty patterns, whose front advances outward with time. Furthermore, by employing a diffusion reaction equation with a nonlinear diffusion coefficient, I could also obtain a more complex dense branched morphology. This branching morphology was found to be emphasized if the effect of random fluctuation in bacterial density are taken into consideration.