A renormalisation approach to excitable reaction-diffusion waves in fractal media

Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice

Existence and stability of reaction-diffusion waves on a fractal lattice

This paper discusses reaction-diffusion wave propagation in fractal lattices, of infinite generation level. We describe how an input/output renormalisation approach can be used to investigate the existence of travelling waves. We also develop a framework for discussing the stability of these travelling waves