Abstract
In the present study, we have formulated a phase description of a neuronal oscillator with non-instantaneous synaptic inputs, by using the phase sensitivity function. By numerical simulation, we found that the synaptic time constant is an important factor for global network synchronization. If the synaptic time constant is smaller, perfectly synchronized behavior quickly occurs. As the synaptic time constant is increased, periodic synchronization emerges. However, synchronized activity is lost for larger synaptic time constant. The external periodic stimulation can change the synchronized patterns in the neuronal population. With a stronger stimulation or high-frequency stimulation, synchronized bursting occurred in the neuronal population.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Buzsaki G. (2006), Rhythms of the brain, Oxford University Press.
Hammod C. et al. (2007) Trends Neuroscience. 30, 357–364.
Fries, P. (2002), J. Neurosci. 22, 3739–3754.
Gray C.M. (1994), J Comput Neurosci. 1, 11–38.
Maldonado, P.E. et al. (2000), Cereb. Corter. 10, 1117–1131.
Dutkin, B. S. et al. (2005), J. Neurophysiol. 94, 1623–1635.
A.T.Winfree. (1980), The Geometry of Biological Time. Springer, New York.
Y. Kuramoto. (1984) Chemical Oscillations, Waves, and Turbulence. Springer, New York.
E. M. Izhikevich. (2007), Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT Press, Cambridge.
Roy M. Smeal et al. (2010), Phil.R.Soc.B. 365, 407–2422.
Roberto F. Galan et al. (2005), Phy. Rev. Lett. 94, 158101–4.
Yasuhiro Tsubo et al. (2007), Euro. J. Neurosci. 25, 3429–3441.
Yauhiro Tsubo et al. (2007), Phy. Rev. Lett. 99, 228101.
G. B. Ermentrout et al. (2008), Trends Neurosci. 31, 428.
A. Pikovsky et al. (2001), Cambridge University Press, Cambridge.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 11232005 and No. 11172086.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Jiao, X., Zhu, D., Wang, R. (2015). Synchronization in Neuronal Population with Phase Response. In: Liljenström, H. (eds) Advances in Cognitive Neurodynamics (IV). Advances in Cognitive Neurodynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9548-7_36
Download citation
DOI: https://doi.org/10.1007/978-94-017-9548-7_36
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-9547-0
Online ISBN: 978-94-017-9548-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)