We study time-periodic forcing of spatially-extended patterns near aTuring-Hopf bifurcation point. A symmetry-based normal form analysis yieldsseveral predictions, including that (i) weak forcing near the intrinsic Hopffrequency enhances or suppresses the Turing amplitude by an amount that scalesquadratically with the forcing strength, and (ii) the strongest effect is seenfor forcing that is detuned from the Hopf frequency. To apply our results tospecific models, we perform a perturbation analysis on general two-componentreaction-diffusion systems, which reveals whether the forcing suppresses orenhances the spatial pattern. For the suppressing case, our results explainfeatures of previous experiments on the CDIMA chemical reaction. However, wealso find examples of the enhancing case, which has not yet been observed inexperiment. Numerical simulations verify the predicted dependence on theforcing parameters.
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