Phase reduction approach to elastohydrodynamic synchronization of beating flagella

Yoji Kawamura and Remi Tsubaki
Phys. Rev. E 97, 022212 – Published 12 February 2018

Abstract

We formulate a theory for the phase reduction of a beating flagellum. The theory enables us to describe the dynamics of a beating flagellum in a systematic manner using a single variable called the phase. The theory can also be considered as a phase reduction method for the limit-cycle solutions in infinite-dimensional dynamical systems, namely, the limit-cycle solutions to partial differential equations representing beating flagella. We derive the phase sensitivity function, which quantifies the phase response of a beating flagellum to weak perturbations applied at each point and at each time. Using the phase sensitivity function, we analyze the phase synchronization between a pair of beating flagella through hydrodynamic interactions at a low Reynolds number.

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  • Received 12 July 2017

DOI:https://doi.org/10.1103/PhysRevE.97.022212

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Nonlinear Dynamics

Authors & Affiliations

Yoji Kawamura1,2,* and Remi Tsubaki2

  • 1Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
  • 2Research and Development Center for Marine Biosciences, Japan Agency for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan

  • *ykawamura@jamstec.go.jp

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Issue

Vol. 97, Iss. 2 — February 2018

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