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.

(joint work with Kjartan G. Magnusson and Sven Sigurdsson at the University of Iceland) (Paper)