Mathematical models for self-organization of biological groups

It is observed that coherent motions like bird flocks and fish schools are common phenomena in biology. Recently, many mathematical models have been developed in order to understand the mechanisms that lead to such coordinated motions. In this thesis I consider two models based on the Langevin equation with different external forces. In these Lagrangian models the motion of the group is determined by pairwise interactions. For the first model we perform an $H$-stability analysis, recover a wide range of interesting patterns and study the state transition induced by noise. The second model contains a different interaction potential. We perform a weak noise limit and study the case when the potential has random coefficients. We also derive the continuous versions of the deterministic cases of these models by using statistical mechanical theory.