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Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type arederived in a mean-field-type limit from stochastic, moderately interactingmany-particle systems for multiple population species in the whole space. Thediffusion term in the stochastic model depends nonlinearly on the interactionsbetween the individuals, and the drift term is the gradient of theenvironmental potential. In the first step, the mean-field limit leads to anintermediate nonlocal model. The local cross-diffusion system is derived in thesecond step in a moderate scaling regime, when the interaction potentialsapproach the Dirac delta distribution. The global existence of strong solutionsto the intermediate and the local diffusion systems is proved for sufficientlysmall initial data. Furthermore, numerical simulations on the particle levelare presented.

Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems