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An Information-Theoretic Approach to Collective Behaviors

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Design and Control of Swarm Dynamics

Part of the book series: SpringerBriefs in Complexity ((BRIEFSCOMPLEXITY))

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Abstract

Swarming agents are interconnected organisms or agents. As is well known in our information age, a key benefit of being connected is access to information. We have discovered and observed this interconnectivity from the biological standpoint in Chap. 2, then analyzed it from the physical viewpoint in Chap. 3, and thoroughly studied its network structure and dynamics in Chap. 4. Such dynamic interconnectivity serves the purpose of channeling information exchanges, which are critical to the effectiveness in swarming. Indeed, it is well known that collective animal behavior is dependent on the existence of communication channels enabling information exchange between individuals (Krause, Ruxton, Living in Groups, Oxford Series in Ecology and Evolution, 2002). For instance, the collective surveillance against oncoming threats of a flock of birds provides a higher level of vigilance only if the information obtained by each pair of eyes is shared among the flock. However, up to now our discussion about information was limited to generalities and we have not detailed the following: (i) the role of information in collective behaviors, (ii) how information is communicated throughout a swarm, and (iii) how information is processed or computed in a decentralized way by the swarm. This chapter is concerned with (i) and (ii), while the next one will deal with distributed information processing from the perspective of decision-making or collective computation.

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Notes

  1. 1.

    Equivalent to information update since the Nyquist rate \(2B=f\) relates bandwidth and frequency of update.

References

  1. J. Krause, G.D. Ruxton, Living in Groups, Oxford Series in Ecology and Evolution (Oxford University Press, Oxford, 2002)

    Google Scholar 

  2. A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, T.S. Grigera, A. Jelić, S. Melillo, L. Parisi, O. Pohl, E. Shen, M. Viale, Information transfer and behavioural inertia in starling flocks. Nat. Phys. 10, 691–696 (2014)

    Article  Google Scholar 

  3. D.J.T. Sumpter, Collective Animal Behavior (Princeton University Press, Princeton, 2010)

    Book  MATH  Google Scholar 

  4. A. Strandburg-Peshkin, C. Twomey, N. Bode, A. Kao, Y. Katz, C. Ioannou, S. Rosenthal, C. Torney, H. Wu, S. Levin, I. Couzin, Visual sensory networks and effective information transfer in animal groups. Curr. Biol. 23(17), R709–R711 (2013)

    Article  Google Scholar 

  5. D. Sumpter, J. Buhl, D. Biro, I. Couzin, Information transfer in moving animal groups. Theory Biosci. 127, 177–186 (2008)

    Article  Google Scholar 

  6. N.W.F. Bode, J.J. Faria, D.W. Franks, J. Krause, A.J. Wood, How perceived threat increases synchronization in collectively moving animal groups. Proc. R. Soc. B 277, 3065–3070 (2010)

    Article  Google Scholar 

  7. N.O. Handegard, K.M. Boswell, C.C. Ioannou, S.P. Leblanc, D.B. Tjøstheim, I.D. Couzin, The dynamics of coordinated group hunting and collective information transfer among schooling prey. Curr. Biol. 22, 1213–1217 (2012)

    Article  Google Scholar 

  8. C. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27(379–423), 623–656 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  9. I.D. Couzin, J. Krause, N.R. Franks, S.A. Levin, Effective leadership and decision making in animal groups on the move. Nature 433, 513–516 (2005)

    Article  Google Scholar 

  10. J.E. Herbert-Read, J. Buhl, F. Hu, A.J.W. Ward, D.J.T. Sumpter, Initiation and spread of escape waves within animal groups. R. Soc. Open Sci. 2, 140355 (2015)

    Article  Google Scholar 

  11. D. Radakov, Schooling in the Ecology of Fish (Wiley, New York, 1973)

    Google Scholar 

  12. P. Holme, J. Saramäki, Temporal networks. Phys. Rep. 519, 97–125 (2012)

    Article  Google Scholar 

  13. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proc. Natl. Acad. Sci. USA 105, 1232–1237 (2008)

    Article  Google Scholar 

  14. M. Komareji, R. Bouffanais, Resilience and controllability of dynamic collective behaviors. PLoS One 8, e82578 (2013)

    Article  Google Scholar 

  15. M. Komareji, R. Bouffanais, Controllability of a swarm of topologically interacting autonomous agents. Int. J. Complex Syst. Sci. 3, 11–19 (2013)

    Google Scholar 

  16. Y. Shang, R. Bouffanais, Influence of the number of topologically interacting neighbors on swarm dynamics. Sci. Rep. 4, 4184 (2014)

    Article  Google Scholar 

  17. G.N. Nair, F. Fagnani, S. Zampieri, R.J. Evans, Feedback control under data rate constraints: an overview. Proc. IEEE 95(1), 108–137 (2007)

    Article  Google Scholar 

  18. W.S. Wong, R.W. Brockett, Systems with finite communication bandwidth constraints—part I: estimation problems. IEEE Trans. Autom. Control 42(9), 1294–1299 (1997)

    Article  MATH  Google Scholar 

  19. R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)

    Article  Google Scholar 

  20. J.P. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)

    Article  Google Scholar 

  21. A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48, 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  22. W. Ren, R. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50, 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  23. A. Scholz, N. Kuboyama, G. Hempelmann, W. Vogel, Complex blockade of TTX-resistant Na\(^+\) currents by lidocaine and bupivacaine reduce firing frequency in Drg neurons. J. Neurophysiol. 279, 1746–1754 (1998)

    Google Scholar 

  24. D.B. Dusenbery, Sensory Ecology: How Organisms Acquire and Respond to Information (W.H. Freeman and Co., New York, 1992)

    Google Scholar 

  25. Y. Shang, R. Bouffanais, Consensus reaching in swarms ruled by a hybrid metric-topological distance. Eur. Phys. J. B 87, 294 (2014)

    Article  MathSciNet  Google Scholar 

  26. J. Baillieul, P.J. Antsaklis, Control and communication challenges in networked real-time systems. Proc. IEEE 95(1), 9–28 (2007)

    Article  Google Scholar 

  27. D. MacKay, Information Theory, Inference, and Learning Algorithms (Cambridge University Press, Cambridge, 2003)

    MATH  Google Scholar 

  28. E. Meyer, E.-G. Neumann, Physical and Applied Acoustics (Academic Press, New York, 1972)

    Google Scholar 

  29. C. Papadimitriou, K. Steiglitz, Ch. 6.1 The max-flow, min-cut theorem, Combinatorial Optimization: Algorithms and Complexity (Dover Publications, New York, 1998), pp. 117–120

    Google Scholar 

  30. C. Glass, C. Wardle, W. Mojsiewicz, A light intensity threshold for schooling in the Atlantic mackerel, scomber scombrus. J. Fish Biol. 29, 71–81 (1986)

    Google Scholar 

  31. M. Keenleyside, Some aspects of the schooling behaviour of fish. Behaviour 8, 183–248 (1955)

    Article  Google Scholar 

  32. A. Emery, Preliminary comparisons of day and night habits of freshwater fish in Ontario lakes. J. Fish. Res. Board Can. 30, 761–774 (1973)

    Article  Google Scholar 

  33. T. Vicsek, A. Zafeiris, Collective motion. Phys. Rep. 517, 71–140 (2012)

    Article  Google Scholar 

  34. G. Grégoire, H. Chaté, Onset of collective and cohesive motion. Phys. Rev. Lett. 92, 025702 (2004)

    Article  Google Scholar 

  35. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Novel type of phase-transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)

    Article  MathSciNet  Google Scholar 

  36. C. McCann, P. Kriebel, C. Parent, W. Losert, Cell speed, persistence and information transmission during signal relay and collective migration. J. Cell Sci. 123, 1724–1731 (2010)

    Article  Google Scholar 

  37. E.O. Wilson, Chemical communication among workers of the fire ant Solenopsis saevissima (Fr. Smith). 1. The organization of mass-foraging. Anim. Behav. 10, 134–147 (1962)

    Article  Google Scholar 

  38. E. Bonabeau, M. Dorigo, G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems (Oxford University Press, Oxford, 1999)

    MATH  Google Scholar 

  39. G.F. Young, L. Scardovi, A. Cavagna, I. Giardina, N.E. Leonard, Starling flock networks manage uncertainty in consensus at low cost. PLoS Comput. Biol. 9(1), e1002894 (2013)

    Article  MathSciNet  Google Scholar 

  40. M. Komareji, Y. Shang, R. Bouffanais, Swarming collapse under limited information flow between individuals, (September 2014). arXiv:1409.7207

  41. R. Solé, Phase Transitions (Princeton University Press, Princeton, 2011)

    MATH  Google Scholar 

  42. D.J.T. Sumpter, The principles of collective animal behaviour. Philosophical Trans. R. Soc. B 361, 5–22 (2006)

    Article  Google Scholar 

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  1. Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore, 487372, Singapore

    Roland Bouffanais

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Bouffanais, R. (2016). An Information-Theoretic Approach to Collective Behaviors. In: Design and Control of Swarm Dynamics. SpringerBriefs in Complexity. Springer, Singapore. https://doi.org/10.1007/978-981-287-751-2_5

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  • DOI: https://doi.org/10.1007/978-981-287-751-2_5

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