caa a22 4500 475805399 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s003320010005 doi (NATIONALLICENCE)springer-10.1007/s003320010005 Translational Symmetry-Breaking for Spiral Waves [Elektronische Daten] [V. G. LeBlanc, C. Wulff] Summary. : Spiral waves are observed in numerous physical situations, ranging from Belousov-Zhabotinsky (BZ) chemical reactions, to cardiac tissue, to slime-mold aggregates. Mathematical models with Euclidean symmetry have recently been developed to describe the dynamic behavior (for example, meandering) of spiral waves in excitable media. However, no physical experiment is ever infinite in spatial extent, so the Euclidean symmetry is only approximate. Experiments on spiral waves show that inhomogeneities can anchor spirals and that boundary effects (for example, boundary drifting) become very important when the size of the spiral core is comparable to the size of the reacting medium. Spiral anchoring and boundary drifting cannot be explained by the Euclidean model alone. In this paper, we investigate the effects on spiral wave dynamics of breaking the translation symmetry while keeping the rotation symmetry. This is accomplished by introducing a small perturbation in the five-dimensional center bundle equations (describing Hopf bifurcation from one-armed spiral waves) which is SO(2)-equivariant but not equivariant under translations. We then study the effects of this perturbation on rigid spiral rotation, on quasi-periodic meandering and on drifting. Springer-Verlag New York Inc., 2000 LeBlanc V. G. Department of Mathematics, University of Ottawa, Ottawa, ON K1N 6N5, Canada, CA aut Wulff C. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, D - 14195 Berlin, Germany, DE aut Journal of Nonlinear Science Springer-Verlag 10/5(2000-10-01), 569-601 0938-8974 10:5<569 2000 10 332 https://doi.org/10.1007/s003320010005 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003320010005 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- LeBlanc V. G. Department of Mathematics, University of Ottawa, Ottawa, ON K1N 6N5, Canada, CA aut NATIONALLICENCE 700 1- Wulff C. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, D - 14195 Berlin, Germany, DE aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/5(2000-10-01), 569-601 0938-8974 10:5<569 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer