Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities

Abstract: We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing chemotactic movement) and a secreting state (producing the attractant). We show that the switching rate provides a powerful mechanism for controlling the densities of spontaneously emerging aggregates. Specifically, in two- and three-dimensional settings it is shown that when both switching rates coincide and are suitably large, then the densities of both the chemotaxing and the secreting population will exceed any prescribed level at some points in the considered domain. This is complemented by two results asserting the absence of such aggregation phenomena in corresponding scenarios in which one of the switching rates remains within some bounded interval.