Scholarlink

<p>The so-called <i>Filament-Based Lamellipodium Model</i> is a complex modeling framework for a very heterogeneous chemo-mechanical system of cell biology. It contains a model for Coulomb repulsion between filaments, whose effect on the stability of the system has been unclear. In this work, a strongly simplified version of the model is considered, showing a destabilizing effect of the repulsion. This instability results in a pitchfork bifurcation with an additional rotational symmetry, leading to a two-dimensional bifurcating manifold of traveling wave solutions. The simplified model is derived, its linearization around the trivial steady state is analyzed, and a formal bifurcation analysis is carried out. It is shown that the pitchfork bifurcation may be super- or subcritical. Time-dependent numerical simulations illustrate these results and provide additional, more global information on the emergence of periodic and chaotic dynamics by secondary bifurcations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pitchfork Bifurcation and Traveling Waves for a Planar Ensemble of Rigid Filaments with Repulsive Interaction

  • 期刊论文

  • 发表日期：

    2026年7月8日

查看全文
  • Gervy Marie Angeles,
  • Jared Barber,
  • Christian Schmeiser

摘要

The so-called Filament-Based Lamellipodium Model is a complex modeling framework for a very heterogeneous chemo-mechanical system of cell biology. It contains a model for Coulomb repulsion between filaments, whose effect on the stability of the system has been unclear. In this work, a strongly simplified version of the model is considered, showing a destabilizing effect of the repulsion. This instability results in a pitchfork bifurcation with an additional rotational symmetry, leading to a two-dimensional bifurcating manifold of traveling wave solutions. The simplified model is derived, its linearization around the trivial steady state is analyzed, and a formal bifurcation analysis is carried out. It is shown that the pitchfork bifurcation may be super- or subcritical. Time-dependent numerical simulations illustrate these results and provide additional, more global information on the emergence of periodic and chaotic dynamics by secondary bifurcations.