We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of @math -dimensional lattice differential equations with unidirectional coupling. This class of lattice equations includes some spatial discretizations for hyperbolic conservation laws with a source term as well as a subclass of monotone systems. We obtain a variational characterization of the critical wave speed above which monotone traveling wave solutions are guaranteed to exist. We also discuss non-monotone waves, and the coexistence of monotone and non-monotone waves.
It is shown that many of the asymptotic properties of the Fisher model for population genetics and population ecology can also be derived for a class of models in which time is discrete and space may or may not be discrete. This allows one to discuss the behavior of models in which the data consist of occasional counts on survey tracts, as well as that of computer models.