Turing's diffusive threshold in random reaction-diffusion systems
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arXiv
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| Natura: | Preprint |
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2020
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| _version_ | 1866910053046419456 |
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| author | Haas, Pierre A. Goldstein, Raymond E. |
| author_facet | Haas, Pierre A. Goldstein, Raymond E. |
| contents | Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here we ask whether this diffusive threshold lowers for $N>2$ to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases $N\leqslant 6$, we find that the diffusive threshold becomes more likely to be smaller and physical as $N$ increases and that most of these many-species instabilities cannot be described by reduced models with fewer species. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_04614 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Turing's diffusive threshold in random reaction-diffusion systems Haas, Pierre A. Goldstein, Raymond E. Soft Condensed Matter Pattern Formation and Solitons Populations and Evolution Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here we ask whether this diffusive threshold lowers for $N>2$ to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases $N\leqslant 6$, we find that the diffusive threshold becomes more likely to be smaller and physical as $N$ increases and that most of these many-species instabilities cannot be described by reduced models with fewer species. |
| title | Turing's diffusive threshold in random reaction-diffusion systems |
| topic | Soft Condensed Matter Pattern Formation and Solitons Populations and Evolution |
| url | https://arxiv.org/abs/2011.04614 |