The Feed-Forward Chain as a Filter-Amplifier Motif

  • Martin Golubitsky
  • LieJune Shiau
  • Claire Postlethwaite
  • Yanyan Zhang
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 3)


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.


Periodic Solution Normal Form Hair Cell Hopf Bifurcation Bifurcation Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • LieJune Shiau
  • Claire Postlethwaite
  • Yanyan Zhang
  1. 1.Mathematical Biosciences InstituteOhio State UniversityColumbusUSA

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