Journal of Statistical Physics

, Volume 151, Issue 3–4, pp 395–413 | Cite as

Modeling Insurgent Dynamics Including Heterogeneity

A Statistical Physics Approach
Article

Abstract

Despite the myriad complexities inherent in human conflict, a common pattern has been identified across a wide range of modern insurgencies and terrorist campaigns involving the severity of individual events—namely an approximate power-law xα with exponent α≈2.5. We recently proposed a simple toy model to explain this finding, built around the reported loose and transient nature of operational cells of insurgents or terrorists. Although it reproduces the 2.5 power-law, this toy model assumes every actor is identical. Here we generalize this toy model to incorporate individual heterogeneity while retaining the model’s analytic solvability. In the case of kinship or team rules guiding the cell dynamics, we find that this 2.5 analytic result persists—however an interesting new phase transition emerges whereby this cell distribution undergoes a transition to a phase in which the individuals become isolated and hence all the cells have spontaneously disintegrated. Apart from extending our understanding of the empirical 2.5 result for insurgencies and terrorism, this work illustrates how other statistical physics models of human grouping might usefully be generalized in order to explore the effect of diverse human social, cultural or behavioral traits.

Keywords

Many-body Social dynamics Conflict 

References

  1. 1.
    Kenney, M.: From Pablo to Osama: Trafficking and Terrorist Networks, Government Bureaucracies, and Competitive Adaptation. University of Pennsylvania Press, Philadelphia (2007) Google Scholar
  2. 2.
    Robb, J.: Brave New War: The Next Stage of Terrorism and the End of Globalization. Wiley, New York (2007) Google Scholar
  3. 3.
    Kilcullen, D.: The Accidental Guerrilla: Fighting Small Wars in the Midst of a Big One. Oxford University Press, London (2009) Google Scholar
  4. 4.
    Hammes, T.X.: The Sling and the Stone, on War in the 21st Century. Zenith, St. Paul (2004) Google Scholar
  5. 5.
    Gambetta, D.: Codes of the Underworld: How Criminals Communicate. Princeton University Press, Princeton (2009) Google Scholar
  6. 6.
    The globalization of crime: a transnational organized crime threat assessment, 2010, United Nations Office on Drugs and Crime United Nations publication No. E.10.IV.6. ISBN 978-92-1-130295-0 Google Scholar
  7. 7.
    Raab, J., Milward, H.B.: Dark networks as problems. J. Public Adm. Res. Theory 13, 413 (2003) CrossRefGoogle Scholar
  8. 8.
    Stewart, S.: Defining Al Qaeda, Stratfor’s Security Weekly, Oct 18, 2012 Google Scholar
  9. 9.
    Bohorquez, J.C., Gourley, S., Dixon, A., Spagat, M., Johnson, N.: Common ecology quantifies human insurgency. Nature 462, 911 (2009) ADSCrossRefGoogle Scholar
  10. 10.
    Johnson, N., Spagat, M., Restrepo, J., Bohorquez, J., Suarez, N., Restrepo, E., Zarama, R.: From old wars to new wars and global terrorism, e-print available at http://arxiv.org/abs/physics/0506213 (2005)
  11. 11.
  12. 12.
    Richardson, L.F.: In: Wright, Q., Lienau, C.C. (eds.) Statistics of Deadly Quarrels. Boxwood Press, Pittsburgh (1960) Google Scholar
  13. 13.
    Cederman, L.: Modeling the size of wars: from billiard balls to sandpiles. Am. Polit. Sci. Rev. 97, 135 (2003) CrossRefGoogle Scholar
  14. 14.
    Clauset, A., Young, M., Gleditsch, K.S.: On the frequency of severe terrorist events. J. Confl. Resolut. 51, 1 (2007) CrossRefGoogle Scholar
  15. 15.
    Spirling, A.: The next big thing: scale invariance in political science. Working paper http://www.people.fas.harvard.edu/~spirling/documents/powerlawSend.pdf (2012)
  16. 16.
    Bouchaud, J.P., Potters, M.: Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management. Cambridge University Press, Cambridge (2004) Google Scholar
  17. 17.
    Mantegna, R.N., Stanley, H.E.: Scaling behaviour in the dynamics of an economic index. Nature 376, 46 (1995) ADSCrossRefGoogle Scholar
  18. 18.
    Johnson, N.F., Jefferies, P., Hui, P.M.: Financial Market Complexity. Oxford University Press, London (2003) CrossRefGoogle Scholar
  19. 19.
    Hedstrom, P., Ylikoski, P.: Causal mechanisms in the social sciences. Annu. Rev. Sociol. 36, 49 (2010) CrossRefGoogle Scholar
  20. 20.
    Norkus, Z.: Mechanisms as miracle makers? The rise and inconsistencies of the ‘mechanismic approach’ in social science and history. Hist. Theory 44, 348 (2005) CrossRefGoogle Scholar
  21. 21.
    Eguiluz, V.M., Zimmerman, M.G.: Transmission of information and herd behavior. Phys. Rev. Lett. 85, 5659 (2000) ADSCrossRefGoogle Scholar
  22. 22.
    D’Hulst, R., Rodgers, G.J.: Exact solution of a model for crowding and information transmission in financial markets. Int. J. Theor. Appl. Finance 3, 609 (2000) MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Axelrod, R.: The dissemination of culture: a model with local convergence and global polarization. J. Confl. Resolut. 41, 203 (1997) CrossRefGoogle Scholar
  24. 24.
    Centola, D., González-Avella, J.C., Eguiluz, V.M., Miguel, M.S.: Homophily, cultural drift, and the co-evolution of cultural groups. J. Confl. Resolut. 51, 905 (2007) CrossRefGoogle Scholar
  25. 25.
    Apolloni, A., Gargiulo, F.: Diffusion processes through social groups’ dynamics. Adv. Complex Syst. 14, 151 (2011) MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wyld, A., Rodgers, G.J.: Models for random graphs with variable strength edges. Physica A 374, 491 (2007) ADSCrossRefGoogle Scholar
  27. 27.
    Tadic, B., Rodgers, G.J.: Modelling conflicts with cluster dynamics on networks. Physica A 389, 5495 (2010) ADSCrossRefGoogle Scholar
  28. 28.
    Johnson, N.F.: Escalation, timing and severity of insurgent and terrorist events: toward a unified theory of future threats. http://arxiv.org/abs/1109.2076
  29. 29.
    Clauset, A., Wiegel, F.W.: A generalized aggregation-disintegration model for the frequency of severe terrorist attacks. J. Confl. Resolut. 54, 179 (2010) CrossRefGoogle Scholar
  30. 30.
    Clauset, A., Gleditsch, K.S.: The developmental dynamics of terrorist organizations. PLoS ONE 7, e48633 (2012) ADSCrossRefGoogle Scholar
  31. 31.
    Johnson, N., Carran, S., Botner, J., Fontaine, K., Laxague, N., Nuetzel, P., Turnley, J., Tivnan, B.: Pattern in escalations in insurgent and terrorist activity. Science 333, 81 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    Lichbach, M.I.: Nobody cites nobody else: mathematical models of domestic political conflict. Defence Econ. 3, 341 (1992) CrossRefGoogle Scholar
  33. 33.
    Asal, V., Rethemeyer, R.K.: The nature of the beast: organizational structures and the lethality of terrorist attacks. J. Polit. 70, 437 (2008) CrossRefGoogle Scholar
  34. 34.
    Kalyvas, S.N.: The Logic of Violence in Civil War. Cambridge University Press, Cambridge (2006) CrossRefGoogle Scholar
  35. 35.
    Kalyvas, S.N.: The paradox of terrorism in civil war. J. Ethics 8, 97 (2004) CrossRefGoogle Scholar
  36. 36.
    Bueno de Mesquita, E.: The political economy of terrorism: a selective overview of recent work. Polit. Economist 10, 112 (2008) Google Scholar
  37. 37.
    Bueno de Mesquita, E.: Conciliation, counterterrorism, and patterns of terrorist violence. Int. Organ. 59, 145 (2005) CrossRefGoogle Scholar
  38. 38.
    Kalyvas, S.N., Kocher, M.A.: The dynamics of violence in Vietnam: an analysis of the Hamlet Evaluation System (HES). J. Peace Res. 46, 335 (2009) CrossRefGoogle Scholar
  39. 39.
    Kaplan, E.H.: Tactical prevention of suicide bombings in Israel (2001–2003). National Academy of Sciences, IED workshops. http://dels.nas.edu/comm/bcst/ieds/pdfs/Kaplan.pdf
  40. 40.
    Kaplan, E.H., Mintz, A., Mishal, S., Samban, C.: What happened to suicide bombings in Israel? Studies in Conflict and Terrorism 28, 225 (2005) CrossRefGoogle Scholar
  41. 41.
    Lyall, J.: Does indiscriminate violence incite insurgent attacks? J. Confl. Resolut. 53, 331 (2009) CrossRefGoogle Scholar
  42. 42.
    Horgan, J.: Divided We Stand: The Psychology and Strategy of Ireland’s Dissident Terrorists. Oxford University Press, New York (2013) CrossRefGoogle Scholar
  43. 43.
    Carley, K.: Destabilizing terrorist networks. In: Proceedings of the 8th International Command and Control Research and Technology Symposium, National Defense War College, Washington, DC, 2003 Google Scholar
  44. 44.
    McCulloh, I.A., Carley, K.M., Webb, M.: Social network monitoring of Al-Qaeda. Network Sci. 1, 25 (2007) Google Scholar
  45. 45.
    Weinstein, J.M.: Inside Rebellion: The Politics of Insurgent Violence. Cambridge University Press, Cambridge (2007) Google Scholar
  46. 46.
    Cederman, L.E., Gleditsch, K.S.: Conquest and regime change: an evolutionary model of the spread of democracy and peace. Int. Stud. Q. 48, 603 (2004) CrossRefGoogle Scholar
  47. 47.
    Johnson, D.D.P., Tierney, D.: The Rubicon theory of war: how the path to conflict reaches the point of no return. Int. Secur. 36, 7 (2011) CrossRefGoogle Scholar
  48. 48.
    Johnson, D.D.P., Weidmann, N.B., Cederman, L.E.: Fortune favours the bold: an agent-based model reveals adaptive advantages of overconfidence in war. PLoS ONE 6, e20851 (2011) CrossRefGoogle Scholar
  49. 49.
    Drapeau, M.D., Hurley, P.C., Armstrong, R.E.: So many zebras, so little time: ecological models and counterinsurgency operations. Defense Horiz. 62, 1 (2008) Google Scholar
  50. 50.
    Lanchester, F.W.: Mathematics in warfare. World Math. 4, 2138 (1956) Google Scholar
  51. 51.
    Kress, M.: Modeling armed conflicts. Science 336, 865 (2012) ADSCrossRefGoogle Scholar
  52. 52.
    Epstein, J.: Nonlinear Dynamics, Mathematical Biology and Social Sciences. Addison-Wesley, Reading (1997) Google Scholar
  53. 53.
    MacKay, N.: Lanchester combat models. Math. Today 42, 170 (2006) MathSciNetGoogle Scholar
  54. 54.
    Gutfraind, A.: Understanding terrorist organizations with a dynamic model. Studies in Conflict and Terrorism 32, 45 (2009) CrossRefGoogle Scholar
  55. 55.
    Lim, M., Metzler, R., Bar-Yam, Y.: Global pattern formation and ethnic/cultural violence. Science 317, 1540 (2007) ADSCrossRefGoogle Scholar
  56. 56.
    Krapivsky, P.L., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010) MATHCrossRefGoogle Scholar
  57. 57.
    Palla, G., Barabasi, A.L., Vicsek, T.: Quantifying social group evolution. Nature 446, 664 (2007) ADSCrossRefGoogle Scholar
  58. 58.
    Forsyth, D.R.: Group Dynamics. Wadsworth, Belmont (2009) Google Scholar
  59. 59.
    Aureli, F., Schaffner, C.M., Boesch, C., Bearder, S.K., Call, J., Chapman, C.A., Connor, R., Di Fiore, A., Dunbar, R.I.M., Henzi, S.P., Holekamp, K., Korstjens, A.H., Layton, R., Lee, P., Lehmann, J., Manson, J.H., Ramos-Fernandez, G., Strier, K.B., van Schaik, C.P.: Fission–fusion dynamics: new research frameworks. Curr. Anthropol. 49, 627 (2008) CrossRefGoogle Scholar
  60. 60.
    Ispolatov, I., Krapivsky, P.L., Redner, S.: War: the dynamics of vicious civilizations. Phys. Rev. E 54, 1274 (1996) ADSCrossRefGoogle Scholar
  61. 61.
    Caro, T.: Antipredator Defenses in Birds and Mammals. University of Chicago Press, Chicago (2005) Google Scholar
  62. 62.
    Fleming, L., Colfer, L., Marin, A., McPhie, J.: Why the Valley went first: aggregation and emergence in regional inventor networks. In: Padgett, J.F., Powell, W.W. (eds.) The Emergence of Organizations and Markets, pp. 520–544. Princeton University Press, Princeton (2012) Google Scholar
  63. 63.
    Ruszczycki, B., Zhao, Z., Burnett, B., Johnson, N.F.: Relating the microscopic rules in coalescence-fragmentation models to the cluster-size distribution. Eur. Phys. J. B 72, 289 (2009) ADSCrossRefGoogle Scholar
  64. 64.
    Zheng, D., Hui, P.M., Johnson, N.F.: Non-universal scaling in a model of information transmission and herd behavior. Eur. Phys. J. B 27, 213 (2002) ADSGoogle Scholar
  65. 65.
    Zhao, Z., Bohorquez, J.C., Dixon, A., Johnson, N.F.: Anomalously slow attrition times for asymmetric populations with internal group dynamics. Phys. Rev. Lett. 103, 148701 (2009) ADSCrossRefGoogle Scholar
  66. 66.
    Dixon, A., Zhao, Z., Bohorquez, J.C., Denney, R., Johnson, N.F.: Statistical physics and modern human warfare. In: Naldi, G., et al. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, pp. 365–396. Birkhäuser, Boston (2010) CrossRefGoogle Scholar
  67. 67.
    Johnson, N.F., Xu, C., Zhao, Z., Ducheneaut, N., Yee, N., Tita, G., Hui, P.M.: Human group formation in online guilds and offline gangs driven by a common team. Phys. Rev. E 79, 066117 (2009) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Neil F. Johnson
    • 1
  • Pedro Manrique
    • 1
  • Pak Ming Hui
    • 2
  1. 1.Physics DepartmentUniversity of MiamiCoral GablesUSA
  2. 2.Physics DepartmentChinese University of Hong KongHong KongChina

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