State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System

Details State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System

2006-06-11

arxiv.org/abs/nlin/0606031v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1016/j.physd.2007.05.007

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, in a definitive way, connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-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.

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