Some mathematical models for flagellar activation mechanisms
Numerical Analysis
2025-04-17 v2 Numerical Analysis
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2409.03506,
title = {Some mathematical models for flagellar activation mechanisms},
author = {François Alouges and Irene Anello and Antonio DeSimone and Aline Lefebvre-Lepot and Jessie Levillain},
journal= {arXiv preprint arXiv:2409.03506},
year = {2025}
}