Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction
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| Format: | Preprint |
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2026
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| _version_ | 1866918389215133696 |
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| author | Angeles, Gervy Marie Barber, Jared Schmeiser, Christian |
| author_facet | Angeles, Gervy Marie Barber, Jared Schmeiser, Christian |
| contents | 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 maybe super- or sub-critical. Time dependent numerical simulations illustrate these results and provide additional, more global information on the emergence of periodic and chaotic dynamics by secondary bifurcations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_24001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction Angeles, Gervy Marie Barber, Jared Schmeiser, Christian Dynamical Systems Analysis of PDEs 35B32, 37L10, 35C07 (Primary) 35Q92, 92C17 (Secondary) 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 maybe super- or sub-critical. Time dependent numerical simulations illustrate these results and provide additional, more global information on the emergence of periodic and chaotic dynamics by secondary bifurcations. |
| title | Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction |
| topic | Dynamical Systems Analysis of PDEs 35B32, 37L10, 35C07 (Primary) 35Q92, 92C17 (Secondary) |
| url | https://arxiv.org/abs/2602.24001 |