Induction of patterns through crowding in a cross-diffusion model

Abstract

In this paper we focus on pattern formation in systems of interacting populations. We show that if one considers these populations to be “crowded” in a way that is defined below, then cross-diffusion terms appear naturally. Moreover, we show that these additional cross-diffusion terms can generate stable spatial patterns that are not manifest in the corresponding standard “dilute” formulation. This result demonstrates the need for care when choosing standard Fickian diffusion as the default in applications to population dynamics.