Subcritical Turing bifurcation and the morphogenesis of localised patterns
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909643740020736 |
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| author | Breña-Medina, Víctor Champneys, Alan |
| author_facet | Breña-Medina, Víctor Champneys, Alan |
| contents | Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing source and loss effects are included in a typical reaction-diffusion system, leading to a super/subcritical transition. Implications are discussed for a range of physical problems, arguing that subcriticality leads to naturally robust phase transitions to localised patterns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subcritical Turing bifurcation and the morphogenesis of localised patterns Breña-Medina, Víctor Champneys, Alan Pattern Formation and Solitons Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing source and loss effects are included in a typical reaction-diffusion system, leading to a super/subcritical transition. Implications are discussed for a range of physical problems, arguing that subcriticality leads to naturally robust phase transitions to localised patterns. |
| title | Subcritical Turing bifurcation and the morphogenesis of localised patterns |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2506.07855 |