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The method of simplest equation is applied for analysis of a class oflattices described by differential-difference equations that admittraveling-wave solutions constructed on the basis of the solution of theRiccati equation. We denote such lattices as Riccati lattices. We search forRiccati lattices within two classes of lattices: generalized Lotka - Volterralattices and generalized Holling lattices. We show that from the class ofgeneralized Lotka - Volterra lattices only the Wadati lattice belongs to theclass of Riccati lattices. Opposite to this many lattices from the Hollingclass are Riccati lattices. We construct exact traveling wave solutions on thebasis of the solution of Riccati equation for three members of the class ofgeneralized Holing lattices.

On traveling waves in lattices: The case of Riccati lattices