In Garcia Guirao and Lampart (J Math Chem 48:159-164, 2010) considered a lattice dynamical system which is stated by Kaneko (Phys Rev Lett 65:1391-1394, 1990) and related to the Belusov-Zhabotinskii reaction. In this note, we introduce the new concepts of density one transitivity and density one weak mixing which are stronger forms of topological transitivity and explore the following more general lattice dynamical systems:
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