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