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The Feed-Forward Chain as a Filter-Amplifier Motif

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Book cover Coherent Behavior in Neuronal Networks

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 3))

Abstract

Hudspeth, Magnasco, and collaborators have suggested that the auditory system works by tuning a collection of hair cells near Hopf bifurcation, but each with a different frequency. An incoming sound signal to the cochlea then resonates most strongly with one of these hair cells, which then informs the auditory neuronal system of the frequency of the incoming signal. In this chapter, we discuss two mathematical issues. First, we describe how periodic forcing of systems near a point of Hopf bifurcation is generally more complicated than the description given in these auditory system models. Second, we discuss how the periodic forcing of coupling identical systems whose internal dynamics is each tuned near a point of Hopf bifurcation leads naturally to successive amplification of the incoming signal. We call this coupled system a feed-forward chain and suggest that it is a mathematical candidate for a motif.

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Acknowledgments

We thank Gemunu Gunaratne, Krešimir Josić, Edgar Knobloch, Mary Silber, Jean-Jacques Slotine, and Ian Stewart for helpful conversations. This research was supported in part by NSF Grant DMS-0604429 and ARP Grant 003652-0009-2006.

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Authors and Affiliations

  1. Mathematical Biosciences Institute, Ohio State University, 1735 Neil Avenue, Columbus, OH, 43210, USA

    Martin Golubitsky

Authors
  1. Martin Golubitsky
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  2. LieJune Shiau
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  3. Claire Postlethwaite
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  4. Yanyan Zhang
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Corresponding author

Correspondence to Martin Golubitsky .

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Editors and Affiliations

  1. Dept. Mathematics, University of Houston, Phillip G. Hoffman Hall 651, Houston, 77204-3008, U.S.A.

    Kre¿imir Josic

  2. Dept. Mathematics, University of Pittsburgh, Thackeray Hall 301, Pittsburgh, 15260, U.S.A.

    Jonathan Rubin

  3. Universitat de les Illes Balears, CSIC, Palma de Mallorca, 07122, Spain

    Manuel Matias

  4. Instituto de Fisiología Celular, Universidad Nacional Autónoma de México, Mexico, 04510, Mexico

    Ranulfo Romo

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Golubitsky, M., Shiau, L., Postlethwaite, C., Zhang, Y. (2009). The Feed-Forward Chain as a Filter-Amplifier Motif. In: Josic, K., Rubin, J., Matias, M., Romo, R. (eds) Coherent Behavior in Neuronal Networks. Springer Series in Computational Neuroscience, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0389-1_6

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