Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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.
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.
Fan, Y.S., Chay, T.R. Generation of periodic and chaotic bursting in an excitable cell model. Biol. Cybern. 71 (1994) 3–431.
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.
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.
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.
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.
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.
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.
Kantz, H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185 (1994) 3–87.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gu, H., Lu, Q. (2008). Identify Stochastic Bursting from Chaotic Bursting Generated in an Experimental Neural Pacemaker. In: Wang, R., Shen, E., Gu, F. (eds) Advances in Cognitive Neurodynamics ICCN 2007. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8387-7_144
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8387-7_144
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8386-0
Online ISBN: 978-1-4020-8387-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)