Transition fronts of two species competition lattice systems in random media

The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave speeds of such transition fronts. We first establish comparison principle for sub-solutions and super-solutions of the related cooperative system. Next, under some proper assumptions, we construct appropriate sub-solutions and super-solutions for the cooperative system. Finally, we show that random transition fronts exist if their least mean speed is greater than an explicit threshold and there is no random transition front with least mean speed less than the threshold.