Identify Stochastic Bursting from Chaotic Bursting Generated in an Experimental Neural Pacemaker

  • Huaguang Gu
  • Qishao Lu
Conference paper


The stochastic and chaotic bursting lying between period k and period k + 1 bursting (k = 2, 3) exhibit similar characteristics such as positive Lyapunov exponent, non-periodic spike trains and deterministic structures such as periodic orbit. The distinctions are identified as different evolutions of the periodic orbit and multi-peaked histogram exhibited in stochastic bursting. The results give practical indicators to distinguish the chaotic bursting and stochastic bursting.


Chaotic bursting stochastic bursting period adding bifurcation periodic orbit lyaponov exponent 


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  1. 1.
    Yang, M.H., An, S.C., Gu, H.G., Liu, Z.Q., Ren, W. Understanding of physiological neural firing through dynamical bifurcation machineries. NeuroReport 17 (2006) 3–999.Google Scholar
  2. 2.
    Fan, Y.S., Holden, A.V. Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity. Chaos, Solitons, Fractals 3 (1993) 439–449.CrossRefGoogle Scholar
  3. 3.
    Fan, Y.S., Chay, T.R. Generation of periodic and chaotic bursting in an excitable cell model. Biol. Cybern. 71 (1994) 3–431.CrossRefGoogle Scholar
  4. 4.
    Ren, W., Hu, S.J., Zhang, B.J., Wang, F.Z. Periodadding bifurcation with chaos in the inter-spike intervals generated by an experimental neural pacemaker. Int. J. Bifurcat. Chaos. 7 (1997) 3–1872.Google Scholar
  5. 5.
    Ren, W., Gu, H.G., Jian, Z., Lu, Q.S., Yang, M.H. Different classification of UPOs in the parametrically different chaotic ISI series. NeuroReport 12 (2001) 3–2124.CrossRefGoogle Scholar
  6. 6.
    Gu, H.G., Yang, M.H., Li, L., Liu, Z.Q., Ren, W. Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios. Phys. Lett. A 319 (2003) 3–96.CrossRefGoogle Scholar
  7. 7.
    Yang, M.H., Gu, H.G., Li, L., Liu, Z.Q., Ren, W. Characteristics of period adding bifurcation without chaos in firing pattern transitions in an experimental neural pacemaker. NeuroReport 14 (2003) 3–2157.CrossRefGoogle Scholar
  8. 8.
    Gu, H.G., Ren, W., Lu, Q.S., Yang, M.H., Chen, W.J. Integer multiple spiking in neural pacemakers without external periodic stimulation. Phys. Lett. A. 285 (2001) 3–68.CrossRefGoogle Scholar
  9. 9.
    So, P., Francis, J.T., Netoff, T.I., Gluckman, B.J., Schiff, S.J. Periodic orbits: a new language for neuronal dynamics, Biophys. J. 74 (1998) 3–2785.CrossRefGoogle Scholar
  10. 10.
    Kantz, H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185 (1994) 3–87.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Huaguang Gu
    • 1
  • Qishao Lu
  1. 1.School of scienceBeihang UniversityBeijing 100083China

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