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Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

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Abstract

Self-sustained oscillations in complex networks consisting of nonoscillatory nodes have attracted long-standing interest in diverse natural and social systems. We study the self-sustained periodic oscillations in random networks consisting of excitable nodes. We reveal the underlying dynamic structure by applying a dominant phase-advanced driving method. The oscillation sources and wave propagation paths can be illustrated clearly via the dynamic structure revealed. Then we are able to control the oscillations with surprisingly high efficiency based on our understanding.

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References

  1. L. Glass, Nature, 2001, 410: 277

    Article  ADS  Google Scholar 

  2. M. B. Elowitz and S. Leibler, Nature, 2000, 403: 335

    Article  ADS  Google Scholar 

  3. A. I. Selverston and M. Moulins, Ann. Rev. Physiol., 1985, 47: 29

    Article  Google Scholar 

  4. G. Buzsáki and A. Draguhn, Nature, 2004, 304: 1926

    Google Scholar 

  5. T. P. Vogels, K. Rajan, and L. F. Abbott, Ann. Rev. Neurosci., 2005, 28: 357

    Article  Google Scholar 

  6. G. A. Worrell, L. Parish, S. D. Cranstoun, R. Jonas, G. Baltuch, and B. Litt, Brain, 2004, 127: 1496

    Article  Google Scholar 

  7. T. J. Lewis and J. Rinzel, Network: Comput. Neural Syst., 2000, 11: 299

    Article  Google Scholar 

  8. A. Roxin, H. Riecke, and S. A. Solla, Phys. Rev. Lett., 2004, 92: 198101

    Article  ADS  Google Scholar 

  9. S. Sinha, J. Saramäki, and K. Kaski, Phys. Rev. E, 2007, 76: 015101 (R)

    Article  ADS  Google Scholar 

  10. A. J. Steele, M. Tinsley, and K. Showalter, Chaos, 2006, 16: 015110

    Article  ADS  MathSciNet  Google Scholar 

  11. A. Zeng, Y. Q. Hu, and Z. R. Di, Phys. Rev. E, 2010, 81: 046121

    Article  ADS  Google Scholar 

  12. G. Bianconi, N. Gulbahce, and A. E. Motter, Phys. Rev. Lett., 2008, 100: 118701

    Article  ADS  Google Scholar 

  13. X. J. Ma, L. Huang, Y.-C. Lai, and Z. G. Zheng, Phys. Rev. E, 2009, 79: 056106

    Article  ADS  Google Scholar 

  14. M. J. O’Donovan, Curr. Opin. Neurobiol., 1999, 9: 94

    Article  Google Scholar 

  15. M. V. Sanchez-Vives and D. A. McCormick, Nature Neurosci., 2000, 3: 1027

    Article  Google Scholar 

  16. X. H. Liao, W. M. Ye, X. D. Huang, Q. Z. Xia, X. H. Huang, P. F. Li, Y. Qian, X. Q. Huang, and G. Hu, arXiv: 0906.2356, 2009

  17. Y. Qian, X. D. Huang, G. Hu, and X. H. Liao, Phys. Rev. E, 2010, 81: 036101

    Article  ADS  Google Scholar 

  18. D. J. Watts and S. H. Strogatz, Nature, 1998, 393: 440

    Article  ADS  Google Scholar 

  19. B. Bollobás, Modern Graph Theory: Springer-Verlag, 1998

  20. W. M. Ye, X. D. Huang, X. H. Huang, P. F. Li, Q. Z. Xia, and G. Hu, Phys. Lett. A, 2010, 374: 2521

    Article  ADS  Google Scholar 

  21. R. Fitzhugh, Biophys. J., 1961, 1: 445

    Article  ADS  Google Scholar 

  22. E. M. Izhikevich, IEEE Trans. on Neural Networks, 2004, 15: 1063

    Article  Google Scholar 

  23. M. Bär and M. Eiswirth, Phys. Rev. E, 1993, 48: R1635

    Article  ADS  Google Scholar 

  24. A.-L. Barabási and R. Albert, Science, 1999, 286: 509

    Article  MathSciNet  Google Scholar 

  25. M. Müller-Linow, C. C. Hilgetag, and M. T. Hütt, PLoS Comput. Biol., 2008, 4: e1000190

    Article  Google Scholar 

  26. M. Kuperman and G. Abramson, Phys. Rev. Lett. 2001, 86: 2909

    Article  ADS  Google Scholar 

  27. J. M. Greenberg and S. P. Hastings, SIAM J. Appl. Math., 1978, 34: 515

    Article  MATH  MathSciNet  Google Scholar 

  28. P. Bak, K. Chen, and C. Tang, Phys. Lett. A, 1990, 147: 297

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Beijing Normal University, Beijing, 100875, China

    Xu-hong Liao  (廖旭红), Yuan-yuan Mi  (弭元元), Qin-zhi Xia  (夏勤智), Xiao-qing Huang  (黄晓清) & Gang Hu  (胡岗)

  2. Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji, 721007, China

    Yu Qian  (钱郁)

Authors
  1. Xu-hong Liao  (廖旭红)
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  2. Yu Qian  (钱郁)
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  3. Yuan-yuan Mi  (弭元元)
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  4. Qin-zhi Xia  (夏勤智)
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  5. Xiao-qing Huang  (黄晓清)
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  6. Gang Hu  (胡岗)
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Corresponding author

Correspondence to Gang Hu  (胡岗).

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Liao, Xh., Qian, Y., Mi, Yy. et al. Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes. Front. Phys. China 6, 124–132 (2011). https://doi.org/10.1007/s11467-010-0152-1

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  • DOI: https://doi.org/10.1007/s11467-010-0152-1

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