Kinetic FRG Young Researchers Workshop
March 2-5, 2009

CSIC Building (#406), Seminar Room 4122.

From Individual to Macroscopic Models in Animal Displacements

Dr. Sébastien Motsch

University Paul Sabatier, Toulouse

Abstract:  In this talk, we first recall classical models for animal displacement and we point the necessity of a new model for fish motion, the so-called "Persistent turning walker" (PTW) model. Using a multiscale approach, we explain how to derive a diffusive equation starting from the PTW model. Some numerical simulations will illustrate the theory.

 In a second part, we investigate a minimal model introduced by Vicsek et al. describing alignment rule between particles. This model is used for example to describe fish interaction (combined with an attraction-repulsion rule). Despite its simplicity a lot of questions are opened about it and in particular what is the dynamic at a larger scale. Our first work is to derive a continuous time-dependent equation starting from this algorithm. Then, using again a multiscale approach, we explain how to derive a macroscopic model from this individual dynamic. After some explanations about the specificity of the hyperbolic equation obtained, we introduce the numerical challenges for resolving this equation. Finally, we compare numerical simulations of the model both at the particle and macroscopic level.