Abstract
Spiral waves in excitable media are typically observed to rotate at a unique angular frequency ω around an effective hole region of radius ro. We investigate the selection problem for ro and ω in the large ro limit of the free-boundary problem of wave propagation in excitable media for the case where the recovery variable is non-diffusive. Analytical forms are derived for the dependence of ro and ω on the usual small parameter ε (which measures the abruptness of excitation) and a parameter A which measures the excitability of the medium. Where spiral wave solutions cease to exist we find a new class of solutions to the free-boundary problem analogous in shape to the Saffman-Taylor fingers of viscous hydrodynamics. These solutions correspond physically to wave fronts with a retracting tip structure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. J. Field and M. Burger, Oscillations and Traveling Waves in Chemical Systems (Wiley, New York, 1985).
A.T. Winfree, When Time Breaks Down (Princeton University Press, New Jersey, 1987).
V.S. Zykov, Simulation of Wave Processes in Excitable Media (Manchester University Press, New York, 1987).
A.S. Mikhailov and V.I. Krinsky, Physica 9D, 346 (1983).
J. P. Keener and J. J. Tyson, Physica 21D, 307 (1986).
J.J. Tyson and J. P. Keener, Physica 32D, 327 (1988).
A. T. Winfree, to appear in Physics Letters A.
A. Karma, Phys. Rev. Lett. 65, 2824 (1990).
P. C. Fife, J. Stat. Phys. 39, 687 (1985).
J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).
D. A. Kessler and H. L. Levine, Physica 39D, 1 (1989).
G. Nash and M. E. Glicksman, Acta Metall. 22, 1283 (1974).
P. Pelce and J. Sun, (to appear in Physica D).
A. Karma (to be published).
J. J. Tyson and J. P. Keener, Physica 29D, 215 (1987).
A. M. Pertsov, E. A. Ermakova, and A.V. Panfilov, Physica 14D, 117 (1984).
A. Karma (to be published).
A.T. Winfree, Science 175, 634 (1972).
S.C. Muller, T. Plesser, and B. Hess, Physica 24D, 87 (1987).
G.S. Skinner and H.L. Swinney (to appear in Physica D).
W. Jahnke, W.E. Skaggs, and A.T. Winfree, J. Phys. Chem. 93, 740 (1989).
E. Lugosi, Physica 40D, 331 (1989).
D. Barkley, M. Kness, and L. Tukerman, Phys, Rev, A42, 2489 (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Plenum Press, New York
About this chapter
Cite this chapter
Karma, A. (1991). Velocity Selection in Two-Dimensional Excitable Media: From Spiral Waves to Retracting Fingers. In: Amar, M.B., Pelcé, P., Tabeling, P. (eds) Growth and Form. NATO ASI Series, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1357-1_26
Download citation
DOI: https://doi.org/10.1007/978-1-4684-1357-1_26
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-1359-5
Online ISBN: 978-1-4684-1357-1
eBook Packages: Springer Book Archive