Invariant Multiparameter Sensitivity of Oscillator Networks

  • Kenzaburo Fujiwara
  • Takuma Tanaka
  • Kiyohiko Nakamura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8834)

Abstract

The behavior of neuronal and other biological systems is determined by their parameter values. We introduce a new metric to quantify the sensitivity of output to parameter changes. This metric is referred to as invariant multiparameter sensitivity (IMPS) because it takes on the same value for a class of equivalent systems. As a simplification of neuronal membrane, we calculate, in parallel resistor circuits, the values of IMPS and a previously studied metric of parameter sensitivity. Furthermore, we simulate phase oscillator models on complex networks and clarify the property of IMPS.

Keywords

Parameter Sensitivity Complex Network Phase Oscillator Synchronization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117, 500–544 (1952)Google Scholar
  2. 2.
    Aoyagi, T., Kang, Y., Terada, N., Kaneko, T., Fukai, T.: The role of Ca2 + -dependent cationic current in generating gamma frequency rhythmic bursts: Modeling study. Neuroscience 115, 1127–1138 (2002)CrossRefGoogle Scholar
  3. 3.
    Csete, M.E., Doyle, J.C.: Reverse engineering of biological complexity. Science 295, 1664–1669 (2002)CrossRefGoogle Scholar
  4. 4.
    Leeds, J.V., Ugron, G.: Simplified multiple parameter sensitivity calculation and continuously equivalent networks. IEEE Transactions on Circuit Theory 14, 188–191 (1967)CrossRefGoogle Scholar
  5. 5.
    Roska, T.: Summed-sensitivity invariants and their generation. Electronics Letters 4, 281–282 (1968)CrossRefGoogle Scholar
  6. 6.
    Goddard, P., Spence, R.: Efficient method for the calculation of first- and second-order network sensitivities. Electronics Letters 5, 351–352 (1969)CrossRefGoogle Scholar
  7. 7.
    Rosenblum, A., Ghausi, M.: Multiparameter sensitivity in active RC networks. IEEE Transactions on Circuit Theory 18, 592–599 (1971)CrossRefGoogle Scholar
  8. 8.
    Maeda, K., Kurata, H.: Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks. Journal of Theoretical Biology 272, 174–186 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Goldstein, A., Kuo, F.: Multiparameter sensitivity. IRE Transactions on Circuit Theory 8, 177–178 (1961)CrossRefGoogle Scholar
  10. 10.
    Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Physical Review Letters 94, 018102 (2005)Google Scholar
  11. 11.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49, 1520–1533 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kuramoto, Y.: Chemical oscillations, waves and turbulence. Springer, Berlin (1984)CrossRefMATHGoogle Scholar
  14. 14.
    Teramae, J., Tanaka, D.: Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Physical Review Letters 93, 204103 (2004)CrossRefGoogle Scholar
  15. 15.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  16. 16.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kenzaburo Fujiwara
    • 1
  • Takuma Tanaka
    • 1
  • Kiyohiko Nakamura
    • 1
  1. 1.Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and EngineeringTokyo Institute of TechnologyYokohamaJapan

Personalised recommendations