A computer-assisted study of pulse dynamics in anisotropic media

This study focuses on the computer-assisted stability analysis of travellin g pulse-like structures in spatially periodic heterogeneous reaction-diffus ion media. The physical motivation comes from pulse propagation in thin ann ular domains on a diffusionally anisotropic catalytic surface. The study wa s performed by computing the travelling pulse-like structures as limit cycl es of the spatially discretized PDE, which in turn is performed in two ways : a Newton method based on a pseudospectral discretization of the PDE, and a Newton-Picard method based on a finite difference discretization. Details about the spectra of these modulated pulse-like structures are discussed, including how they may be compared with the spectra of pulses in homogeneou s media. The effects of anisotropy on the dynamics of pulses and pulse pair s are studied. Beyond shifting the location of bifurcations present in homo geneous media, anisotropy can also introduce certain new instabilities. (C) 2001 Elsevier Science B.V. All rights reserved.