MODEL OF AGGREGATION - A Topological Approach

Masud Rana, Dongsheng Cai

Abstract

The aggregate motion of flocks of birds, a herd of land animals, Mexican wave forming in stadia are beautiful and nice examples of collective behaviour. The aggregation is constructed by the action of each individual, each action solely on basis of its local perception of the world. Scientists from different backgrounds have tried to model collective behaviour. Most of the models are strictly metric (based on Euclidian distance among individuals) but flocks of birds do not act on metric perception. In this paper we proposed a model based on topological perspective to construct a flock of birds with large number of individuals and checked flock’s density independent behaviour.

References

  1. Vicsek, T., 2001. “A question of scale”, Nature. vol411.
  2. Farkas, I., Helbing, D. and Vicsek, T., 2002. “Mexican waves in an excitable medium”. Nature. 419, 131-132.
  3. Reynolds, Craig W., 1987. “Flocks, Herds, and Schools: A Distributed Behavioral Model”. ACM Computer Graphics. volume 21, No.4.
  4. Inada, Y. and Kawachi, K., 2002. “Order and Flexibility in the Motion of Fish Schools”. Journal of Theretical Biology. vol.214, issue 13.
  5. Bhattacharya, K. and Vicsek, T., 2010. “Collective decision making in cohesive flocks”. New Journal of Physics. 12 093019.
  6. Moussaid, M., Helbing, D. and Theraulaz, G., 2011, “How simple rules determine pedestrian behavior and crowd disaster”. PNAS. vol. 108, no. 17.
  7. Vicsek, T. et al., 1995. “Novel Type of Phase Transition in a System of Self-Driven Particles”. Phys. Rev. Lett. 75, 1226-1229.
  8. Gönci, B. M. Nagy and Vicsek, T., 2008. “Phase transition in the scalar noise model of collective motion in three dimensions”. The European Physical Journal. Volume 157, Number 1, 53-59.
  9. Vicsek, T., 2008. “Universal Patterns of Collective Motion from Minimal Models of Flocking”. 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems.
  10. Ballerini, M. et al., 2008. “Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study”, PNAS. vol. 105 no. 4 1232-1237.
  11. Simha, R. Aditi and Sriram Ramaswamy, 2002. “Statistical hydrodynamics of ordered suspensions of self-propelled particles: waves, giant number fluctions and instabilities”, Physica A. 306 (2002) 262-269.
  12. O'Brien, D. P., 1989. “Analysis of the internal arrangement of individuals within crustacean aggregations (Euphausiacea, Mysidacea)”, J. Exp. Mar. Biol. Ecol.,Vol. 128, pp. l-30.
  13. http://en.wikipedia.org/wiki/Topology. (26 September, 2011).
  14. http://www.nn.iij4u.or.jp/hsat/techterm/topos.html (26 September, 2011).
  15. Henrikson, A. K, 2002. “Distance and foreign policy: a political geography approach”, Intl. Political Sci. Rev 23, 437.
  16. Vine, I., 1971. “Risk of visual detection and pursuit by a predator and the selective advantage of flocking behaviour”. Journal of Theoretical Biology. Volume 30, Issue 2, Pages 405-422.
  17. Chaté, H., Ginelli, F., Grégoire, G., Peruani, F. and Raynaud, F., 2008. “Modeling collective motion: variations on the Vicsek model”, The European Physical Journal B - Condensed Matter and Complex Systems. Volume 64, Numbers 3-4, 451-456.
  18. Gruler, H., Dewald, U. and Eberhardt, M., “Nematic liquid crystals formed by living amoeboid cells”. The European Physical Journal B - Condensed Matter and Complex Systems. Volume 11, Number 1, 187-192.
  19. Kemkemer, R., Kling, D., Kaufmann, D. and Gruler, H., 2000. “Elastic properties of nematoid arrangements formed by amoeboid cells”. The European Physical Journal E: Soft Matter and Biological Physics. Volume 1, Numbers 2-3, 215-225.
  20. Parrish, J. K. and Hamner, W., 1997. Animal groups in three dimensions. Cambridge University Press.
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Paper Citation


in Harvard Style

Rana M. and Cai D. (2012). MODEL OF AGGREGATION - A Topological Approach . In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012) ISBN 978-989-8565-02-0, pages 355-360. DOI: 10.5220/0003818603550360


in Bibtex Style

@conference{grapp12,
author={Masud Rana and Dongsheng Cai},
title={MODEL OF AGGREGATION - A Topological Approach},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012)},
year={2012},
pages={355-360},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003818603550360},
isbn={978-989-8565-02-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012)
TI - MODEL OF AGGREGATION - A Topological Approach
SN - 978-989-8565-02-0
AU - Rana M.
AU - Cai D.
PY - 2012
SP - 355
EP - 360
DO - 10.5220/0003818603550360