Time-modulated oscillatory structures in phase-separating reactive mixtures.
We investigate the effect of temporal modulation on the spatiotemporal patterns produced by phase separation in chemically reactive ternary mixtures. The temporal modulation is introduced by making one of the reaction rates periodic in time. Our main concern is the stability of traveling waves, which appear above a Hopf-type bifurcation at a finite wave number and are stable in the absence of external modulation. It is shown by computer simulations in two dimensions that when the external modulation is present, various types of coherent standing waves emerge near the special point in the parameter space, where the Turing-type bifurcation line and the Hopf-type bifurcation line meet each other. We carry out a theoretical analysis to understand the phase diagram of the synchronized oscillatory structures obtained numerically.