Dihedral rings of patterns emerging from a Turing bifurcation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914702795210752 |
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| author | Hill, Dan J. Bramburger, Jason J. Lloyd, David J. B. |
| author_facet | Hill, Dan J. Bramburger, Jason J. Lloyd, David J. B. |
| contents | Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns are strongly interacting. We prove that approximate strongly interacting patterns can emerge in various ring-like dihedral configurations, bifurcating from quiescence near a Turing instability in generic two-component reaction-diffusion systems. The methods used are constructive and provide accurate initial conditions for numerical continuation methods to path-follow these ring-like patterns in parameter space. Our analysis is complemented by numerical investigations that illustrate our findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13122 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dihedral rings of patterns emerging from a Turing bifurcation Hill, Dan J. Bramburger, Jason J. Lloyd, David J. B. Dynamical Systems Pattern Formation and Solitons Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns are strongly interacting. We prove that approximate strongly interacting patterns can emerge in various ring-like dihedral configurations, bifurcating from quiescence near a Turing instability in generic two-component reaction-diffusion systems. The methods used are constructive and provide accurate initial conditions for numerical continuation methods to path-follow these ring-like patterns in parameter space. Our analysis is complemented by numerical investigations that illustrate our findings. |
| title | Dihedral rings of patterns emerging from a Turing bifurcation |
| topic | Dynamical Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2210.13122 |