OSCILLATIONS OF FRONTS AND FRONT PAIRS IN 2-COMPONENT AND 3-COMPONENTREACTION-DIFFUSION SYSTEMS

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