Designing reaction-cross-diffusion systems with Turing and wave instabilities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918129284677632 |
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| author | Villar-Sepúlveda, Edgardo Champneys, Alan R. Krause, Andrew L. |
| author_facet | Villar-Sepúlveda, Edgardo Champneys, Alan R. Krause, Andrew L. |
| contents | General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general $n$-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Designing reaction-cross-diffusion systems with Turing and wave instabilities Villar-Sepúlveda, Edgardo Champneys, Alan R. Krause, Andrew L. Pattern Formation and Solitons 35K57, 35B36 General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general $n$-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria. |
| title | Designing reaction-cross-diffusion systems with Turing and wave instabilities |
| topic | Pattern Formation and Solitons 35K57, 35B36 |
| url | https://arxiv.org/abs/2409.06860 |