# American Institute of Mathematical Sciences

March  2011, 4(1): 1-16. doi: 10.3934/krm.2011.4.1

## Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type

 1 Department of Mathematics and Statistics, University of Victoria, PO BOX 3060 STN CSC, Victoria, BC V8W 3R4, Canada, Canada, Canada

Received  August 2010 Revised  November 2010 Published  January 2011

The Cucker-Smale model for flocking or swarming of birds or insects is generalized to scenarios where a typical bird will be subject to a) a friction force term driving it to fly at optimal speed, b) a repulsive short range force to avoid collisions, c) an attractive "flocking" force computed from the birds seen by each bird inside its vision cone, and d) a "boundary" force which will entice birds to search for and return to the flock if they find themselves at some distance from the flock. We introduce these forces in detail, discuss the required cutoffs and their implications and show that there are natural bounds in velocity space. Well-posedness of the initial value problem is discussed in spaces of measure-valued functions. We conclude with a series of numerical simulations.
Citation: Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1
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