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

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