Abstract: The existence and non-existence of generalized traveling waves for two species competitive lattice system in general time inhomogeneous media were considered. By establishing comparison principle for sub-solutions and super-solutions of the related cooperative system and constructing appropriate sub-solutions and super-solutions of the cooperative system, the author proved that the generalized traveling waves of the system  exist when their least mean speed was greater than an explicit threshold, and there was no generalized traveling wave whose least mean speed was less than this threshold.

Key words: competition system, lattice system, generalized traveling wave, existence