Spirals in Scalar Reaction–Diffusion Equations

M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal of Bifurcation and Chaos (1995) 1487–1501.

Download
No fulltext has been uploaded.
Journal Article | Published | English
Author
; ; ;
Abstract
<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>
Publishing Year
Journal Title
International Journal of Bifurcation and Chaos
Page
1487-1501
LibreCat-ID

Cite this

Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos. 1995:1487-1501. doi:10.1142/s0218127495001149
Dellnitz, M., Golubitsky, M., Hohmann, A., & Stewart, I. (1995). Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos, 1487–1501. https://doi.org/10.1142/s0218127495001149
@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar Reaction–Diffusion Equations}, DOI={10.1142/s0218127495001149}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501} }
Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, 1487–1501. https://doi.org/10.1142/s0218127495001149.
M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar Reaction–Diffusion Equations,” International Journal of Bifurcation and Chaos, pp. 1487–1501, 1995.
Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, pp. 1487–501, doi:10.1142/s0218127495001149.

Export

Marked Publications

Open Data LibreCat

Search this title in

Google Scholar