A Two-Species Social Dominance Model

We study the general properties of a stochastic two-species social-domination model defined on a $d$-dimensional lattice. The introduction of spatial degrees of freedom and allowance of stochastic fluctuations surprisingly does not invalidate the deterministic mean-field picture. In the active state, where the dominant and submissive species coexist, no patch formation is observed, with correlation lengths restricted to a few lattice sites. Oscillations seen in the submissive population density are strongly damped and restricted to a small section of the parameter space. Observations are explained to be a result of the two-particle reactions being restricted to the same social group.