Group Dynamics of Phototaxis: Interacting Stochastic Many-Particle Systems and their Continuum Limit

(with D. Bhaya and T. Requeijo)

in S. Benzoni-Gavage and D. Serre (Eds.), "Hyperbolic Problems: Theory, Numerics, Applications", Proc. 11th Int Conf on Hyperbolic Problems, Lyon 2006; Spring-Verlag, Berlin, 2008, 145-159

In this paper we introduce new models for describing the motion of phototaxis, i.e. bacteria that move towards light.   Following experimental observations, the first model describes the locations of bacteria, an internal property of the bacteria that is related to the group dynamics, and the interaction between the bacteria and the medium in which it resides.   The second model is a new multi-particle system following the same quantities as in the first model.  The main theorem shows how to obtain a new system of PDEs, which we refer to as the phototaxis system as the limit dynamics of the multi-particle system.  Numerical simulations are provided.

                                         © Doron Levy 2012