Can primitive chemotaxis generate spatial structures?

Parabolic models for the collective behaviour in populations of chemotactically migrating cells are considered. A focus will be on cases in which individuals are particularly primitive in the sense that beyond a partially oriented movement toward increasing concentrations of a nutrient, furtheractivity can essentially be neglected.

Recent developments in the analysis of such nutrient taxis systems are to be described, with a special emphasis set on mathematical challenges related to the fundamental question how far models of this type are capable of adequately reflecting aspects of colourful dynamics known from experimental observations.