Alternative scenarios of spiral breakup in a reaction-diffusion model withexcitable and oscillatory dynamics

Instabilities (breakup) of spiral waves in two dimensions and their one-dim ensional analogs-wave trains triggered by a specific boundary condition-lea ding to spatiotemporally chaotic dynamics are investigated in a simple acti vator-inhibitor model. These instabilities: always require an absolute inst ability of the emitted wave trains and coincide with the Eckhaus instabilit y for the excitable case, while for oscillatory conditions the well-known c onvective variant of the Eckhaus instability is found. The different cases correspond to different spiral breakup phenomenologies [S0031-9007(99)08410 -0].