Abstract
We consider the effect of periodic external forcing on the spatiotemporal dynamics of one-dimensional oscillatory media modelled by the complex Ginzburg-Landau equation (CGLE). We determine the domain of existence and linear stability of the spatially homogeneous synchronous solution found at strong forcing. Some of the synchronization scenarios observed are described, and the “turbulent synchronized states” encountered are detailed. We show that 2π-phase kinks are the ubiquitous objects mediating synchronization and study their nontrivial dynamics. In particular, we consider the processes of kink-breeding and the spontaneous creation of kinks which are specific to our phase and amplitude description. The general consequences, at the statistical level, of breaking the gauge invariance of the CGLE by a periodic forcing are discussed.
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