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

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.

Keywords

self-sustained oscillations / random networks / excitable nodes / oscillation sources / wave propagation

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

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

[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

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

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

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

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

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

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

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

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

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Higher Education Press and Springer-Verlag Berlin Heidelberg