Influence of boundaries on localized patterns.
We analytically study the influence of boundaries on distant localized patterns generated by a Turing instability. To this end, we use the Swift-Hohenberg model with arbitrary boundary conditions. We find that the bifurcation diagram of these localized structures generally involves four homoclinic s...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2009
|
| _version_ | 1797104604298608640 |
|---|---|
| author | Kozyreff, G Assemat, P Chapman, S |
| author_facet | Kozyreff, G Assemat, P Chapman, S |
| author_sort | Kozyreff, G |
| collection | OXFORD |
| description | We analytically study the influence of boundaries on distant localized patterns generated by a Turing instability. To this end, we use the Swift-Hohenberg model with arbitrary boundary conditions. We find that the bifurcation diagram of these localized structures generally involves four homoclinic snaking branches, rather than two for infinite or periodic domains. Second, steady localized patterns only exist at discrete locations, and only at the center of the domain if their size exceeds a critical value. Third, reducing the domain size increases the pinning range. |
| first_indexed | 2024-03-07T06:36:03Z |
| format | Journal article |
| id | oxford-uuid:f7a86705-c568-4edd-bbed-ab507e3f71f8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:36:03Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:f7a86705-c568-4edd-bbed-ab507e3f71f82022-03-27T12:44:24ZInfluence of boundaries on localized patterns.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f7a86705-c568-4edd-bbed-ab507e3f71f8EnglishSymplectic Elements at Oxford2009Kozyreff, GAssemat, PChapman, SWe analytically study the influence of boundaries on distant localized patterns generated by a Turing instability. To this end, we use the Swift-Hohenberg model with arbitrary boundary conditions. We find that the bifurcation diagram of these localized structures generally involves four homoclinic snaking branches, rather than two for infinite or periodic domains. Second, steady localized patterns only exist at discrete locations, and only at the center of the domain if their size exceeds a critical value. Third, reducing the domain size increases the pinning range. |
| spellingShingle | Kozyreff, G Assemat, P Chapman, S Influence of boundaries on localized patterns. |
| title | Influence of boundaries on localized patterns. |
| title_full | Influence of boundaries on localized patterns. |
| title_fullStr | Influence of boundaries on localized patterns. |
| title_full_unstemmed | Influence of boundaries on localized patterns. |
| title_short | Influence of boundaries on localized patterns. |
| title_sort | influence of boundaries on localized patterns |
| work_keys_str_mv | AT kozyreffg influenceofboundariesonlocalizedpatterns AT assematp influenceofboundariesonlocalizedpatterns AT chapmans influenceofboundariesonlocalizedpatterns |