Abstract.
In this work we study the formation of patterns of neuronal activity when some input are presented to the network. For this task a recently developed model of neuron is utilized. This model requires a very low computational effort but presents many characteristics of more complex models such as, spiking, bursting and sub-threshold oscillations, and therefore the realistic study of the behavior of big ensembles of neurons can be aborded, even under real time conditions. New results of the application of the wavelet transform technique to the analysis of pattern formation and the possible encoding of rhythms are presented; they show that this simple, low-computational, neuron model behaves much like more complex ones.
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References
E.M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (The MIT press, Cambridge, MA, USA, 2007)
B.J. West (ed.), Patterns, Information and Chaos in Neuronal Systems (World Scientific Publishing, Singapore, 1993)
A.C. Scott (ed.), Encyclopedia of Nonlinear Sciences (Routledge, New York, USA, 2004)
A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 165 (1954)
R.M. Rose, J.L. Hindmarsh, Proc. Royal Soc. Lond. B 237, 267 (1989)
M.P. Zorzano, L. Vázquez, Physica D 179, 105 (2003)
L. Vázquez, M.P. Zorzano, FitzHugh-Nagumo, Encyclopedia of Nonlinear Science (Routledge, New York, USA, 2004), p. 307
N.F. Rulkov, Phys. Rev. E 65, 041922–1 (2002)
E.M. Izhikevich, IEEE Trans. Neur. Netw. 14, 1569 (2003)
C. Aguirre, D. Campos, P. Pascual, E. Serrano, Neuro comp. 69, 1116 (2006)
C. Aguirre, D. Campos, P. Pascual, E. Serrano, Lect. Notes Comp. Sci. 3696, 103 (2005)
P. Varona, C. Aguirre, J.J Torres, M.I. Rabinovich, H.D.I. Abarbanel, Neurocom. 44–46, 685 (2002)
E.M. Izhikevich, Int. J. Bifur. Chaos 10, 1171 (2000)
M. Bazhenov, M. Stopfer, M. Rabinovich, R. Huerta, H.D.I. Abarbanel, T.J. Sejnowski, G. Laurent, Neuron 30, 553 (2001)
C.M. Gray, W. Singer, Proc. Natl. Acad. Sci. USA 86, 1698 (1989)
R.C. Elson et al., Phys. Rev. Lett. 81, 5692 (1998)
N.F. Rulkov, I. Timofeev, M. Bazhenov, J. Comp. Neurosci. 17, 203 (2004)
E. Leznik, D. Contreras, V. Makarenko, R. Llinas, Soc. Neurosci. 25, 1252 (1999)
R. Llinás, J.P. Welsh, Curr. Opin. Neurobiol. 3, 958 (1993)
E.J. Stollnitz, T.D. Derose, D.H. Salesin, Wavelets for Computer Graphics (Morgan Kaufman Publishers, Los Altos, CA, USA, 1996)
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Aguirre, C., Campos, D., Pascual, P. et al. Pattern formation and encoding rhythms analysis on a spiking/bursting neuronal network. Eur. Phys. J. Spec. Top. 146, 169–176 (2007). https://doi.org/10.1140/epjst/e2007-00177-8
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DOI: https://doi.org/10.1140/epjst/e2007-00177-8