Ricci flow and nonlinear reaction–diffusion systems in biology, chemistry, and physics

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 modeled 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.