10.1142/s0218127495001149
Dellnitz, Michael
Michael
Dellnitz
Golubitsky, Martin
Martin
Golubitsky
Hohmann, Andreas
Andreas
Hohmann
Stewart, Ian
Ian
Stewart
Spirals in Scalar Reaction–Diffusion Equations
1995
2020-04-15T09:05:30Z
2020-05-19T07:04:07Z
journal_article
https://ris.uni-paderborn.de/record/16551
https://ris.uni-paderborn.de/record/16551.json
0218-1274
<jats:p> 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 (u<jats:sub>r</jats:sub> = mu<jats:sub>θ</jats:sub>). 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. </jats:p>