Title : Individual displacement in biology : a new model for fish
Abstract : In this talk, we start by looking at classical models for
animal displacement (used for ants, cockroaches, fishes...). Those
models don't fit with our experiment data on fishes, therefore we
introduce a new model to describe fish behavior: the so-called
"Persistent Turning Walker" (PTW) model.
Then, we study the long time dynamic of the PTW
model. In this goal, we derive a macroscopic model (a diffusion
equation in this case) from the PTW model, using two different
approaches : firstly with probabilistic tools and secondly with kinetic
Finally, we show recent advances to take into account
interactions between fishes in the PTW model.