Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics

Details Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics

2008-06-13

arxiv.org/abs/0806.2194v6

Nonlinear Sciences

Pattern Formation and Solitons

30 pages, minor changes

Scientific paper

This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction-diffusion processes in biology, chemistry and physics can be modelled by the combined geometric-diffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction-diffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow. Keywords: geometrical Ricci flow, nonlinear reaction-diffusion, dissipative solitons and breathers

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