Dynamics of Aggregating Patterns in a Chemotaxis-Diffusion-Growth Model Equation

Masayasu Mimura¹, Tohru Tsujikawa², Ryo Kobayashi³ and Daishin Ueyama³

¹Department of Mathematical Science, University of Tokyo, Tokyo 153, Japan
²Faculty of Engineering, Hiroshima Denki Institute of Technology, Hiroshima 739-03, Japan
³Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Ohtu 520-21, Japan

(Received August 9, 1993; Accepted September 5, 1993)

Keywords: Aggregating pattern dynamics, Chemotaxis, Layer instability, Interface dynamics

Abstract. Aggregating pattern formation of biological individuals is considered by using a population model equation with diffusion, chemotaxis and growth. From pattern dynamics view point, we numerically study the stability of 2-dimensional localized equilibrium solutions which indicate the dynamics of aggregating patterns of individuals. It is shown that destabilized patterns exhibit very complex patterns such as giraffe like and honeycomb like structures. The interaction of many small clustering patterns is also studied from the chemotactic effect view point.