For the purpose of clarifying the origin of some remarkable wave phenomena arising from chemical activity, a dynamical theory of patterns for a two-component dissipative medium is developed. On two basic assumptions, namely, the existence of a stable limit-cycle oscillation and the slow spatial variation of phase, the kinetic equation is reduced to a form suitable to the analysis of patterns. On the basis of the simplified equation, target patterns, spiral waves, self-locking of phase and solitary wave propagation are discussed from a unified point of view.
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Kuramoto et al. (1976) studied this question.