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A general class of two-component reaction-diffusion systems with excitable dynamics is studied by means of singular perturbation theory. It is shown how stable traveling pulses and periodic wavetrains in one spatial dimension evolve from initial data. This information is applied to two-dimensional regions for which it is shown that steady rotating structures (spirals) exist. The perturbation results are also used to show that a one-dimensional semi-infinite medium exhibits hysteresis when used as a periodic signaling device. Finally, other nonexcitable dynamics are analyzed, and their stable one-dimensional structures listed.
James P. Keener (Mon,) studied this question.
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