We study dynamics of pattern formation in systems belonging to class of reaction-Cattaneo models including persistent diffusion (memory effects of the diffusion flux). It was shown that due to the memory effects pattern seletion process are realized. We have found that oscillatory behavior of the radius of the adsorbate islands is governed by finite propagation speed. It is shown that stabilization of nano-patterns in such models is possible only by nonequilibrium chemical reactions. Oscillatory dynamics of pattern formation is studied in details by numerical simulations.
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