We study the steady states of two stochastic lattice models with two species of particles, where the local mobility of one species depends on the spatial distribution of the other. The eigenvalues of a $2\times 2$ matrix of couplings can develop imaginary parts, and the question arises whether this implies an instability to a macroscopically different steady state. In the first model, where the mobility depends on the local density of the other species, we show that the system undergoes macroscopic phase separation. In the second model, where the mobility depends on the second derivative of the density of the other species, there is a finite correlation length and the density is homogeneous on macroscopic scales.
BARMA, MUNTASİR and RAMASWAMY, SRİRAM (2000) "Steady States of Dynamically Coupled Two-Species Systems," Turkish Journal of Physics: Vol. 24: No. 3, Article 7. Available at: https://journals.tubitak.gov.tr/physics/vol24/iss3/7