Abstract
A Input-Output relationship of a neuron is often used to characterize the function of the neuron. In that case, inputs are assumed to be constant, and neuronal responses to fluctuated inputs are less understood. A recent work reported a strange response of the Hodgkin-Huxley neuron to the fluctuated inputs that an irregularity of spike trains is inversely proportional to an input irregularity. In this paper, we investigated an origin of the strange response by using the Hindmarsh-Rose neuron. We provided the parameter regions for bifurcations and confirmed that the Hindmarsh-Rose neuron reproduces the strange response in dynamics of Saddle-Node and Subcritical Hopf bifurcations. In both bifurcation cases, the Hindmarsh-Rose neuron shows a bistability of resting potential and repetitive firing. This indicates that the bistability is the origin of the strange input-output relationship.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hodgkin, A.L.: Journal of Physiology 107, 165 (1948)
Tuckwell, H.C.: Introduction to theoretical neurobiology. Cambridge University Press, Cambridge (1988)
Shadlen, M.N., Newsome, W.T.: Current Opinion in Neurobiology 4, 569 (1994)
Miura, K., Tsubo, Y., Okada, M., Fukai, T.: Journal of Neuroscience 27, 13802 (2007)
Vogels, T.P., Abbott, L.F.: Nature Neuroscience 12, 483 (2009)
Brown, D., Feng, J., Feerick, S.: Physical Review Letters 82, 4731 (1999)
Hosaka, R., Sakai, Y., Ikeguchi, T., Yoshizawa, S.: Journal of the physical society of Japan 75, 124007 (2006)
Fourcaud-Trocme, N., Hansel, D., van Vreeswijk, C., Brunel, N.: Journal of Neuroscience 23, 11628 (2000)
Shinomoto, S., Tsubo, Y.: Physical Review EÂ 64, 041910 (2001)
Schreiber, S., Samengo, L., Herz, A.V.M.: Journal of Neurophysiology 101, 2239 (2009)
Sakai, Y., Yamada, M., Yoshizawa, S.: Proceedings of International Joint Conference on Neural Networks 2, 1275 (2002)
Tsuji, S., et al.: International Journal of Bifurcation and Chaos 17, 985 (2007)
Izhikevich, E.M.: Dynamical systems in neuroscience: The Geometry of Excitability and Bursting. The MIT Press, Cambridge (2007)
Hindmarsh, J.L., Rose, R.M.: Nature 296, 162 (1982)
Egorov, A.V., et al.: Nature 420, 173 (2002)
Steriade, M., Nunez, A., Amzica, F.: Journal of Neuroscience 13, 2352 (1993)
Guckenheimer, J., Holmes, D.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, Heidelberg (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hosaka, R., Sakai, Y., Aihara, K. (2009). Strange Responses to Fluctuating Inputs in the Hindmarsh-Rose Neurons. In: Leung, C.S., Lee, M., Chan, J.H. (eds) Neural Information Processing. ICONIP 2009. Lecture Notes in Computer Science, vol 5864. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10684-2_45
Download citation
DOI: https://doi.org/10.1007/978-3-642-10684-2_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10682-8
Online ISBN: 978-3-642-10684-2
eBook Packages: Computer ScienceComputer Science (R0)