Synchronization Under Control in Complex Networks for a Panic Model

  • Guillaume CantinEmail author
  • Nathalie Verdière
  • Valentina Lanza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11537)


After a sudden catastrophic event occurring in a population of individuals, panic can spread, persist and become more problematic than the catastrophe itself. In this paper, we explore through a computational approach the possibility to control the panic level in complex networks built with a recent behavioral model. After stating a rigorous theoretical framework, we propose a numerical investigation in order to establish the effect of the topology of the network on this control process, with randomly generated networks, and we compare the panic level for two distinct topology sets on a given network.


Optimal control Numerical computation Dynamical system Complex network Synchronization Panic 


  1. 1.
    Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aric, A., Hagberg, D., Schult, A., Pieter, J.: Exploring network structure, dynamics, and function using networkX. In: Proceedings of the 7th Python in Science Conference (2008)Google Scholar
  3. 3.
    Bruzzone, A.: Perspectives of modeling & applied simulation: modeling, algorithms and simulations: advances and novel researches for problem-solving and decision-making in complex, multi-scale and multi-domain system. J. Comput. Sci. 10, 63–65 (2015)CrossRefGoogle Scholar
  4. 4.
    Cantin, G.: Non identical coupled networks with a geographical model for human behaviors during catastrophic events. Int. J. Bifurcat. Chaos 27(14), 1750213 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cantin, G., et al.: Mathematical modeling of human behaviors during catastrophic events: stability and bifurcations. Int. J. Bifurcat. Chaos 26(10), 1630025 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cantin, G., et al.: Control of panic behavior in a non identical network coupled with a geographical model. In: PhysCon 2017, pp. 1–6. University, Firenze (2017)Google Scholar
  7. 7.
    Fleming, W., Rishel, R.: Deterministic and Stochastic Optimal Control, vol. 1. Springer, Berlin (2012)zbMATHGoogle Scholar
  8. 8.
    Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Springer, New York (2001)CrossRefGoogle Scholar
  9. 9.
    Provitolo, D., et al.: Les comportements humains en situation de catastrophe : de l’observation à la modélisation conceptuelle et mathématique. Cybergeo: Eur. J. Geogr. 735 (2015)Google Scholar
  10. 10.
    Stewart, I., Golubitsky, M., Pivato, M.: Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM J. Appl. Dyn. Syst. 2(4), 609–646 (2003)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Team Commands, Inria Saclay: Bocop: an open source toolbox for optimal control (2017).
  12. 12.
    Yagi, A.: Abstract Parabolic Evolution Equations and Their Applications. Springer, Heidelberg (2009). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées du Havre, Normandie Univ, FR CNRS 3335, ISCNLe HavreFrance

Personalised recommendations