Stability and bifurcation analysis in a mechanochemical model of pattern formation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908867786440704 |
|---|---|
| author | Cygan, Szymon Marciniak-Czochra, Anna Münnich, Finn Oelz, Dietmar |
| author_facet | Cygan, Szymon Marciniak-Czochra, Anna Münnich, Finn Oelz, Dietmar |
| contents | We analyze the stability and bifurcation structure of steady states in a mechanochemical model of pattern formation in regenerating tissue spheroids. The model couples morphogen dynamics with tissue mechanics via a positive feedback loop: mechanical stretching enhances morphogen production, while morphogen concentration modulates tissue elasticity. Global strain conservation implements a nonlocal inhibitory effect, realizing a mechanochemical variant of the local activation--long-range inhibition mechanism. For exponential elasticity-morphogen coupling, the system admits a variational formulation. We prove existence of nonconstant steady states for small diffusion and uniqueness of the homogeneous state for large diffusion. Linear stability analysis shows that only unimodal patterns are stable, while multimodal solutions are unstable. Bifurcation analysis reveals subcritical and supercritical pitchforks, with fold bifurcations generating bistable regimes. Our results demonstrate that mechanochemical feedback provides a robust mechanism for single-peaked pattern formation without requiring a second diffusible inhibitor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09998 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability and bifurcation analysis in a mechanochemical model of pattern formation Cygan, Szymon Marciniak-Czochra, Anna Münnich, Finn Oelz, Dietmar Analysis of PDEs 35B36, 35B32, 35B40, 35B38 We analyze the stability and bifurcation structure of steady states in a mechanochemical model of pattern formation in regenerating tissue spheroids. The model couples morphogen dynamics with tissue mechanics via a positive feedback loop: mechanical stretching enhances morphogen production, while morphogen concentration modulates tissue elasticity. Global strain conservation implements a nonlocal inhibitory effect, realizing a mechanochemical variant of the local activation--long-range inhibition mechanism. For exponential elasticity-morphogen coupling, the system admits a variational formulation. We prove existence of nonconstant steady states for small diffusion and uniqueness of the homogeneous state for large diffusion. Linear stability analysis shows that only unimodal patterns are stable, while multimodal solutions are unstable. Bifurcation analysis reveals subcritical and supercritical pitchforks, with fold bifurcations generating bistable regimes. Our results demonstrate that mechanochemical feedback provides a robust mechanism for single-peaked pattern formation without requiring a second diffusible inhibitor. |
| title | Stability and bifurcation analysis in a mechanochemical model of pattern formation |
| topic | Analysis of PDEs 35B36, 35B32, 35B40, 35B38 |
| url | https://arxiv.org/abs/2602.09998 |