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.
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© 1996 Springer-Verlag
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Wulff, C. (1996). Bifurcation theory of meandering spiral waves. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105437
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DOI: https://doi.org/10.1007/BFb0105437
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