Luis Gomez Nava - LJAD, Université Côte d'Azur - Keywords: Collective motion, imitation, stochastic processes.

Luis Gomez Nava - LJAD, Université Côte d'Azur - Keywords: Collective motion, imitation, stochastic processes.

Contribution title: Emergent collective behaviors induced by imitation.

We study of biological systems which present collective properties. We introduce the idea of internal individual biological clock and we connected this concept with the collective movement of a system of individuals, like a herd of sheep, for example. Our collaboration with a group of biologists at the Toulouse University allowed us to design and perform experiments with small (3,4,8,16,32) and big groups (100,120) of sheep. Using the experimental data and the observations on the field we discovered that in our theory a new concept emerged: the idea of a collective clock of the whole system. This concept allows us to explain the behavior of the small groups and predicts transport properties for the big groups.
To have a better understanding of the dynamics of the system, we study also the mean field approximation and we discover that the collective clock is closely connected with a limit cycle that emerges. This guided us to understand and unveil a Hopf bifucration and the existence of a stable limit cycle.
The whole system becomes more complex when we add a space variable via a Langevin equation in order to model and explain the dynamics seen in the experiments with sheep. In this case, we discover the close connection between the collective clock and a collective stick-slip observed in the numerical simulations of the model.