MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Emerging patterns in a hyperbolic model for locally interacting cell systems

Frithjof Lutscher and Angela Stevens


Morphogenetic processes like, for example, neurulation and gastrulation involve coordinated movements of cells. It is assumed that these processes happen due to long range signaling, although the detailed mechanisms are not completely understood. Therefore, one is interested in biological ``model-systems'' where self-organization of cells and in particular the mechanisms of signaling can be analyzed in greater detail. A major question is whether or not also short range signaling or local interaction of cells can be the cause of coordinated movement and morphogenetic processes. As a model problem we analyze ripple formation of myxobacteria due to purely local interaction, a hypothesis which is discussed in the biological literature. These ripples can be observed before the final aggregation of the bacteria and fruiting body formation takes place.

Our basic mathematical model is a one-dimensional hyperbolic system of Goldstein-Kac type with density dependent coefficients. Conditions for the existence of traveling waves are discussed by means of linear analysis and the construction of invariant domains.


Related publications

2002 Repository Open Access
Frithjof Lutscher and Angela Stevens

Emerging patterns in a hyperbolic model for locally interacting cell systems

In: Journal of nonlinear science, 12 (2002) 6, pp. 619-640