Evaluating the Robustness of Activator-Inhibitor Models for Cluster Head Computation

  • Lidia Yamamoto
  • Daniele Miorandi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6234)


Activator-inhibitor models have been widely used to explain several morphogenetic processes. They have also been used to engineer algorithms for computer graphics, distributed systems and networks. These models are known to be robust to perturbations such as the removal of peaks of chemicals. However little has been reported about their actual quantitative performance under such disruptions.

In this paper we experimentally evaluate the robustness of two well-known activator-inhibitor models in the presence of attacks that remove existing activator peaks. We focus on spot patterns used as distributed models for cluster head computation, and on their potential implementation in chemical computing. For this purpose we derive the corresponding chemical reactions, and simulate the system deterministically.

Our results show that there is a trade-off between both models. The chemical form of the first one, the Gierer-Meinhardt model, is slow to recover due to the depletion of a required catalyst. The second one, the Activator-Substrate model, recovers more quickly but is also more dynamic as peaks may slowly move. We discuss the implications of these findings when engineering algorithms based on morphogenetic models.


Wireless Sensor Network Cluster Head Spot Pattern High Activator Concentration Cluster Head Election 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Abelson, H., et al.: Amorphous computing. Communications of the ACM 43 (2000)Google Scholar
  2. 2.
    Adamatzky, A., Costello, B.D.L., Asai, T.: Reaction-Diffusion Computers. Elsevier Science Inc., New York (2005)Google Scholar
  3. 3.
    Atkins, P., de Paula, J.: Physical Chemistry. Oxford University Press, Oxford (2002)Google Scholar
  4. 4.
    Bar-Yam, Y.: Dynamics of Complex Systems. Westview Press (2003)Google Scholar
  5. 5.
    Deckard, A., Sauro, H.M.: Preliminary Studies on the In Silico Evolution of Biochemical Networks. ChemBioChem 5(10), 1423–1431 (2004)CrossRefGoogle Scholar
  6. 6.
    Deutsch, A., Dormann, S.: Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis. Birkhäuser, Basel (2005)zbMATHGoogle Scholar
  7. 7.
    Dittrich, P.: Chemical Computing. In: Banâtre, J.-P., Fradet, P., Giavitto, J.-L., Michel, O. (eds.) UPP 2004. LNCS, vol. 3566, pp. 19–32. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial Chemistries – A Review. Artificial Life 7(3), 225–275 (2001)CrossRefGoogle Scholar
  9. 9.
    Dormann, S.: Pattern Formation in Cellular Automaton Models. Ph.D. thesis, University of Osnabrück, Dept. of Mathematics/Computer Science (2000)Google Scholar
  10. 10.
    Durvy, M., Thiran, P.: Reaction-diffusion based transmission patterns for ad hoc networks. In: INFOCOM, pp. 2195–2205 (2005)Google Scholar
  11. 11.
    Erciyes, K., et al.: Graph theoretic clustering algorithms in mobile ad hoc networks and wireless sensor networks. Appl. Comput. Math. 6, 162–180 (2007)MathSciNetGoogle Scholar
  12. 12.
    Hyodo, K., Wakamiya, N., Murata, M.: Reaction-diffusion based autonomous control of camera sensor networks. In: Proc. Bionetics, Budapest, Hungary (2007)Google Scholar
  13. 13.
    Koch, A.J., Meinhardt, H.: Biological pattern formation: from basic mechanisms to complex structures. Reviews of Modern Physics 66(4) (1994)Google Scholar
  14. 14.
    Lowe, D., Miorandi, D., Gomez, K.: Activation-inhibition-based data highways for wireless sensor networks. In: Proc. Bionetics. ICST, Avignon (2009)Google Scholar
  15. 15.
    Meinhardt, H.: Models of biological pattern formation. Academic Press, London (1982)Google Scholar
  16. 16.
    Murray, J.D.: Mathematical Biology: Spatial models and biomedical applications. Mathematical Biology, vol. 2. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  17. 17.
    Neglia, G., Reina, G.: Evaluating activator-inhibitor mechanisms for sensors coordination. In: Proc. Bionetics. ICST, Budapest (2007)Google Scholar
  18. 18.
    Pearson, J.E.: Complex patterns in a simple system. Science 261(5118), 189–192 (1993)CrossRefGoogle Scholar
  19. 19.
    Soro, S., Heinzelman, W.B.: Cluster Head Election Techniques for Coverage Preservation in Wireless Sensor Networks. Ad Hoc Networks 7, 955–972 (2009)CrossRefGoogle Scholar
  20. 20.
    Turing, A.M.: The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London B 327, 37–72 (1952)CrossRefGoogle Scholar
  21. 21.
    Yoshida, A., Aoki, K., Araki, S.: Cooperative control based on reaction-diffusion equation for surveillance system. In: Khosla, R., Howlett, R.J., Jain, L.C. (eds.) KES 2005. LNCS (LNAI), vol. 3683, pp. 533–539. Springer, Heidelberg (2005)Google Scholar
  22. 22.
    Yu, J.Y., Chong, P.H.J.: A survey of clustering schemes for mobile ad hoc networks. IEEE Communications Surveys and Tutorials 7, 32–48 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lidia Yamamoto
    • 1
  • Daniele Miorandi
    • 2
  1. 1.Data Mining and Theoretical Bioinformatics Team (FDBT), Image Sciences, Computer Sciences and Remote Sensing Laboratory (LSIIT)University of StrasbourgFrance
  2. 2.Pervasive TeamCREATE-NETTrentoItaly

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