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Some mathematical models for flagellar activation mechanisms
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This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by J\"ulicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included.
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Beating of eukaryotic flagella via Hopf bifurcation of a system of stalled molecular motors
A two-row molecular motor model of a flagellar axoneme loses stability via a Hopf bifurcation, giving spontaneous oscillatory beating.
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