On the coexistence of competing memes in the same social network

We present a model of double viral spreading on a multi -network suitable for modeling the diffusion of competitive memes. The main characteristics of the model is that it allows the possibility of changing from one opinion to another without having to go through an agnostic (susceptible) phase. We analyze the survival of two conflicting memes in the limit of t -> infinity as a function of the viralities of the two memes as well as the rate at which an agent can change from believing one meme to believing the other. The parameter space is divided into four survival regions, depending on which meme survives (none, one of the two, both). We derive exact equations for the boundaries between the regions in the case of regular graphs, and, in the general case, we characterize the behavior for weak and strong memes. One relevant finding is that, contrary to the viral spread model in Sahneh and Scoglio (2014) , the crossover allows the co -existence of two memes in the same network. We present simulations to validate the theoretical results.