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Spirals in scalar reaction-diffusion equations
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UNSPECIFIED (1995) Spirals in scalar reaction-diffusion equations. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 5 (6). pp. 1487-1501. ISSN 0218-1274.
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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 (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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science |
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Journal or Publication Title: | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | ||||
Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | ||||
ISSN: | 0218-1274 | ||||
Official Date: | December 1995 | ||||
Dates: |
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Volume: | 5 | ||||
Number: | 6 | ||||
Number of Pages: | 15 | ||||
Page Range: | pp. 1487-1501 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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