Branches of localized patterned states
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918094988902400 |
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| author | Sandstede, Bjorn |
| author_facet | Sandstede, Bjorn |
| contents | Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized patterned structures lie on a discrete stack of loops or on a single unbounded branch. The framework proposed here also connects closely with continuation algorithms that are often used to verify the hypotheses that guarantee the emergence of localized patterned states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branches of localized patterned states Sandstede, Bjorn Dynamical Systems Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized patterned structures lie on a discrete stack of loops or on a single unbounded branch. The framework proposed here also connects closely with continuation algorithms that are often used to verify the hypotheses that guarantee the emergence of localized patterned states. |
| title | Branches of localized patterned states |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.12277 |