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Formal analysis of resonance entrainment by central pattern generator

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Abstract

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Virginia, 122 Engineer’s Way, Charlottesville, VA, 22904-4746, USA

    Y. Futakata & T. Iwasaki

Authors
  1. Y. Futakata
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  2. T. Iwasaki
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Correspondence to T. Iwasaki.

Additional information

This work is supported by NSF 0237708, NSF 0654070, and NIH/NINDS/CRCNS 1 R01 NS46057-01.

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Futakata, Y., Iwasaki, T. Formal analysis of resonance entrainment by central pattern generator. J. Math. Biol. 57, 183–207 (2008). https://doi.org/10.1007/s00285-007-0151-1

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  • DOI: https://doi.org/10.1007/s00285-007-0151-1

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