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Article
Stability of Large Flocks: an Example
Mathematics and Statistics Faculty Publications and Presentations
  • J. J. P. Veerman, Portland State University
  • F. M. Tangerman, Stony Brook University
Document Type
Pre-Print
Publication Date
1-1-2013
Subjects
  • Perturbation (Mathematics),
  • Multiagent systems -- Stability,
  • Asymptotic theory,
  • Linear differential equations,
  • Nearest neighbor analysis (Statistics)
Disciplines
Abstract
The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then show (within a certain class of systems) that a perturbation in the leader's orbit is almost always amplified exponentially in N as it propagates towards the outlying members of the flock. The only exception is when there is a symmetry present in the interaction: in that case the growth of the perturbation is linear in N.
Description

This work can be found in arXiv: https://arxiv.org/abs/1002.0768

Persistent Identifier
http://archives.pdx.edu/ds/psu/17777
Citation Information
J. J. P. Veerman and F. M. Tangerman. "Stability of Large Flocks: an Example" (2013)
Available at: http://works.bepress.com/jj-veerman/19/