Deterministic limit of a density-dependent population model with triangle type nonlocal cross-diffusion

The deterministic limit of a stochastic model of triangle type nonlocal cross-diffusion is considered. The stochastic model is given by a system with two types of particles whose transition rates depend on their densities. In this paper, we reveal that its deterministic limit is governed by some nonlocal cross-diffusion equation, and show the existence of a solution to this equation by Markov chain approximation method.