DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES

UNIVERSITY OF ALBERTA

MATHEMATICAL BIOLOGY SEMINAR

MONDAY, OCTOBER 18, 2004

3:00 - 4:00 p.m.

CAB 657

Petro Babak

Department of Renewable Resources

University of Alberta

Dynamics of group formation in collective motion of organisms

A mathematical description of the collective motion of organisms using a
density-velocity model is presented. This model consists of a system of
non-linear parabolic equations, a forced Burgers equation for velocity and a
diffusion-convection equation for density. The motion is mainly due to forces
resulting from the differences between local density levels and a prescribed
density level.

The existence of a global attractor for a one-dimensional density-velocity
model is proved by asymptotic analysis to demonstrate different patterns in
the attractors for density. The theoretical results are supplemented with
numerical results. These patterns, which can be characterized into groups,
correspond to movement of collective organized groups of organisms such as
fish schools and bird flocks.