Article ID Journal Published Year Pages File Type
1898185 Physica D: Nonlinear Phenomena 2007 15 Pages PDF
Abstract

We study a class of swarming problems   wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. HH-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
Authors
, , , , ,