Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917872356294656 |
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| author | López-Pedrares, Javier Suárez-Vázquez, Marcos Pérez-Mercader, Juan Muñuzuri, Alberto P. |
| author_facet | López-Pedrares, Javier Suárez-Vázquez, Marcos Pérez-Mercader, Juan Muñuzuri, Alberto P. |
| contents | Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms between the different species involved and transport mechanisms. We present here a mathematical analysis aiming to explore the mathematical constraints that a reaction-diffusion dynamical model should comply in order to exhibit a Turing instability. The main conclusion limits the existence of this instability to nonlinearity degrees larger or equal to three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model López-Pedrares, Javier Suárez-Vázquez, Marcos Pérez-Mercader, Juan Muñuzuri, Alberto P. Pattern Formation and Solitons Mathematical Physics Dynamical Systems Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms between the different species involved and transport mechanisms. We present here a mathematical analysis aiming to explore the mathematical constraints that a reaction-diffusion dynamical model should comply in order to exhibit a Turing instability. The main conclusion limits the existence of this instability to nonlinearity degrees larger or equal to three. |
| title | Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model |
| topic | Pattern Formation and Solitons Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2412.13783 |