Phase waves in oscillatory media

Abstract Oscillation phase spatial distributions influence the behavior of an oscillatory reaction-diffusion system. The dependence of the frequency of oscillations on the constant phase gradient is obtained. It is shown that for small enough values of the phase gradient the frequency is constant and is equal to that of homogeneous bulk oscillations. This can explain target patterns observed in BZ systems. The case of spatially non-uniform phase gradient is also considered. It is shown that there exist solutions corresponding to a moving stationary phase pattern which may be regarded as a secondary solitary wave superimposed on the primary phase waves. This approach helps to explain the details of such transitional processes as collision and displacement of waves with differing frequencies.