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January  2006, 14(1): 31-62. doi: 10.3934/dcds.2006.14.31

Interacting spots in reaction diffusion systems

S.-I. Ei 1, , M. Mimura 2, and  M. Nagayama 3,

1. 

Faculty of Mathematics, Kyushu University, Ropponmatsu Chuo-ku, Fukuoka, 810-8560, Japan
2. 

School of Science and Technology, Meiji University, Higashimita 1-1-1 Tama-ku Kawasaki, 214-8571, Japan
3. 

Graduate School of Natural Science and Technology, Kanazawa University, Kakuma Kanazawa, 920-1192, Japan

Received  September 2004 Revised  February 2005 Published  October 2005

This paper is concerned with the dynamics of travelling spot solutions in two dimensions. Travelling spot solutions are constructed under the bifurcation structure with Jordan block type degeneracy. It is shown that if the velocity is very slow, such travelling spots possess reflection property. In order to do it, we derive the reduced ordinary differential equations describing the dynamics of interacting travelling spots in RD systems by using center manifold theory. This reduction enables us to prove that two very slowly travelling spots reflect before collision as if they were elastic particles.
Keywords: Travelling spots, Reaction diffusion systems, interaction of spots..
Mathematics Subject Classification: Primary: 58F14, 92C15; Secondary: 58D2.
Citation: S.-I. Ei, M. Mimura, M. Nagayama. Interacting spots in reaction diffusion systems. Discrete & Continuous Dynamical Systems, 2006, 14 (1) : 31-62. doi: 10.3934/dcds.2006.14.31
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