Modelling of Collective Animal Behavior Using Relations and Set Theory

  • Jan Nikodem
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8111)


In this paper we focus on developing the formal methods and techniques necessary to model and classify a collective animal behaviour. The benefits of using set theory are the possibility of a formal examination of the local problems and to organize individuals as elements of the considered classes, defined globally. In order to describe collective activity of animals, we proposed concepts of actions, behaviour and structures. To govern collective behaviour of animals we propose three key relations and mappings determined taxonomic order on them.


collective animal bahaviour relations 


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  1. 1.
    Alexander, R.M.: Hitching a lift hydrodynamically - in swimming, flying and cycling. J. Biol. 3(2), article7; BioMed Central Ltd. (2004)Google Scholar
  2. 2.
    Blondel, V., Hendrickx, J.M., Olshevsky, A., Tsitsiklis, J.N.: Convergence in multi-agent coordination, consensus, and flocking. In: Proc. of 44th IEEE Conf. Decision and Control and 2005 Eur. Control Conf (CDC-ECC 2005), pp. 2996–3000 (2005)Google Scholar
  3. 3.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of National Academy of Sciences 99(12), 7821–7826 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Jaron, J.: Systemic Prolegomena to Theoretical Cybernetics: Scientific Papers of Institute of Technical Cybernetics, no. 45, Wroclaw University of Technology (1978)Google Scholar
  5. 5.
    Kuratowski, K., Mostowski, M.: Set Theory, with introduction to descriptive set theory; Studies in Logic and the Foundations of Mathematics, vol. 86. PWN-Warsaw, North-Holland, Amsterdam, New York (1976)Google Scholar
  6. 6.
    Nikodem, J., Chaczko, Z., Nikodem, M., Klempous, R.: Smart and Cooperative Neighbourhood for Spatial Routing in Wireless Sensor Networks. In: Madarász, L., Živčák, J. (eds.) Aspects of Computational Intelligence. TIEI, vol. 2, pp. 167–184. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE 95(1) (2007)Google Scholar
  8. 8.
    Parrish, J.K., Viscido, S.V., Grunbaum, D.: Selforganized fish schools: An examination of emergent properties. Biol. Bull. 202, 296–305 (2002)CrossRefGoogle Scholar
  9. 9.
    Pratt, S.C., Mallon, E.B., Sumpter, D.J.T., Franks, N.R.: Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis. Behav. Ecol. Sociobiol. 52, 117–127 (2002), doi:10.1007/s00265-002-0487-x.CrossRefGoogle Scholar
  10. 10.
    Reynolds, C.W.: Flocks, Herds, and Schools: A Distributed Behavioral Model. In: SIGGRAPH 1987 Conference Proceedings, Computer Graphics, vol. 21(4), pp. 25–34 (1987)Google Scholar
  11. 11.
    Savkin, A.V.: Coordinated collective motion of groups of autonomous mobile robots, Analysis of Vicsek’s model. IEEE Trans. Autom. Control 49(6), 981–982 (2004)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Speakman, J.R., Banks, D.: The function of flight formations in Greylag Geese Anser anser; energy saving or orientation? IBIS 140(2), 280–287 (1998), doi:10.1111/j.1474-919X.1998.tb04390.xCrossRefGoogle Scholar
  13. 13.
    Sumpter, D.J.T.: The principles of collective animal behaviour. Phil. Trans. R. Soc. B 361, 5–22 (2006), doi:10.1098/rstb.2005.1733.CrossRefGoogle Scholar
  14. 14.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel Type of Phase Transition in a System of Self-Driven Particles. Phys. Rev. Lett. 75(6), 1226–1229 (1995)CrossRefGoogle Scholar
  15. 15.
    Wolpert, D., Tumer, K.: An overview of collective intelligence. In: Bradshaw, J.M. (ed.) Handbook of Agent Technology. AAAI Press/MIT Press, Cambridge (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan Nikodem
    • 1
  1. 1.The Institute of Computer Engineering, Control and RoboticsWrocław University of TechnologyWrocławPoland

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