Analytical approximations for spiral waves
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
- OSTI ID:
- 22251732
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 23, Issue 4; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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