Analysis in Kantorovich Geometric Space for Quasi-stable Patterns in 2D-OV Model

Abstract

TheIshiwata, Ryosuke two-dimensional optimalSugiyama, Yuki velocity (2D-OV) model, which consists of self-driven particles, reproduces a big variety of dynamical patterns as seen in biological collective motions (Sugiyama (2009) Natural Computing. Springer Japan, Tokyo [7]). We perform simulations of the 2D-OV model in a simple maze. Dynamically stable patterns are observed from the simulation results. The stability of the patterns seems to be related to a kind of degeneracy of a state. In order to look for some physical quantity, which can indicate the relation between the stability and the degeneracy, we construct a geometric space based on the Kantorovich distance among patterns and represent the changing of flow pattern as the trajectory in the geometric space. As a result, a point corresponding to distributions of particles for the quasi-stable pattern converges to the localised region in the space.