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Bifurcation theory of meandering spiral waves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wulff, Claudia |
| Copyright Year | 1996 |
| Abstract | Spiral waves are a typical phenomenon of spatio-temporal pattern formation. They are observed in various biological and chemical systems, for example in the catalysis on platinum surfaces and in the Belousov-Zhabotinsky reaction. We develop a mathematical theory for the Hopf bifurcation from rigidly rotating spiral waves to meandering spiral waves; we prove the transition to drifting spiral waves if the rotation frequency of the rigidly rotating spiral wave is a multiple of the module of the Hopf eigenvalue and we study the parameter-dependence of the drift velocity near the bifurcation from rigidly rotating spiral waves. Furthermore we prove that analogous phenomena occur if a rigidly rotating spiral wave is subjected to external periodic forcing. Our results hold for a general class of reaction-diffusion systems and provide a rigorous mathematical explanation of experiments on the meandering transition in autonomous and periodically forced systems. |
| Starting Page | 166 |
| Ending Page | 178 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BFb0105437 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/BFb0105437 |
| Alternate Webpage(s) | http://www.math.fu-berlin.de/~Dynamik/preprints/wulff_meander.ps.gz |
| Alternate Webpage(s) | https://doi.org/10.1007/BFb0105437 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
