The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems

The chemotaxis equations are a well-known system of partial differential equations describing aggregation phenomena in biology. In this paper they are rigorously derived from an interacting stochastic many-particle system, where the interaction between the particles is rescaled in a moderate way as population size tends to infinity. The novelty of this result is that in all previous applications of this kind of limiting procedure, the principal part of the system is assumed to fulfill an ellipticity condition which is not satisfied in our case. New techniques which deal with this difficulty are presented.