Spirals in scalar reaction-diffusion equations
UNSPECIFIED. (1995) Spirals in scalar reaction-diffusion equations. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 5 (6). pp. 1487-1501. ISSN 0218-1274Full text not available from this repository.
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(r) = mu(theta)). 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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
|Journal or Publication Title:||INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS|
|Publisher:||WORLD SCIENTIFIC PUBL CO PTE LTD|
|Number of Pages:||15|
|Page Range:||pp. 1487-1501|
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