OSCILLATIONS OF FRONTS AND FRONT PAIRS IN TWO- AND THREE-COMPONENT REACTION-DIFFUSION SYSTEMS

摘要

We investigate multi-component reaction-diffusion systems on a finite one-dimensional domain. The first component is assumed both to react on a short time-scale, and to have a small diffusion length leading to patterns with sharp fronts. To analyze stability, we apply the SLEP method by Nishiura and Fujii. This method is superior to standard perturbation methods. We illustrate this using a two-component system. In the three-component system, in a situation where both the influence of the first component on the other components and the interaction of the latter is only weak, we show that there is a unique Hopf destabilization of stationary fronts when changing time constants. As an example we treat a system with global coupling used e.g. for semi-conductor devices. For filaments (front pairs) we find two types of Hopf destabilizations: breathing and swinging. The global coupling controls which type occurs. This corresponds to recent experimental results and is confirmed via numerical calculations. [References: 28]