---
res:
bibo_abstract:
- Spiral patterns have been observed experimentally, numerically, and theoretically
in a variety of systems. It is often believed that these spiral wave patterns
can occur only in systems of reaction–diffusion equations. We show, both theoretically
(using Hopf bifurcation techniques) and numerically (using both direct simulation
and continuation of rotating waves) that spiral wave patterns can appear in a
single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral"
boundary conditions (ur = muθ). Spiral
boundary conditions are motivated by assuming that a solution is infinitesimally
an Archimedian spiral near the boundary. It follows from a bifurcation analysis
that for this form of spirals there are no singularities in the spiral pattern
(technically there is no spiral tip) and that at bifurcation there is a steep
gradient between the "red" and "blue" arms of the spiral. @eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Michael
foaf_name: Dellnitz, Michael
foaf_surname: Dellnitz
- foaf_Person:
foaf_givenName: Martin
foaf_name: Golubitsky, Martin
foaf_surname: Golubitsky
- foaf_Person:
foaf_givenName: Andreas
foaf_name: Hohmann, Andreas
foaf_surname: Hohmann
- foaf_Person:
foaf_givenName: Ian
foaf_name: Stewart, Ian
foaf_surname: Stewart
bibo_doi: 10.1142/s0218127495001149
dct_date: 1995^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0218-1274
- http://id.crossref.org/issn/1793-6551
dct_language: eng
dct_title: Spirals in Scalar Reaction–Diffusion Equations@
...