Abstract
The nonlinear interactions of solitary wavefronts in excitable media are determined by the manner of recovery to the rest state. The distance between a pair of wavefronts tends to lock at one of countably many possible values in the case of oscillatory recovery, while it increases indefinitely when the recovery is monotonic. We derive these results from the basic reaction diffusion equations and study the implications on pattern formation in one and two space dimensions. In particular we demonstrate how spatiotemporal complexity may arise in one dimension, and discuss possible consequences of the interplay between wavefront-interactions and curvature in two dimensions.
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References
Tyson, J.J. & Keener, J.P. (1988). Physica D (Amsterdam) 32, 327.
Miller, R.N. & Rinzel, J. (1981). Biophys. J. 34, 227.
Rinzel, J. & Maginu, K. (1984). In Non-Equilibrium Dynamics in Chemical Systems, Vidal, C. & Pacault, (eds.). Springer: Berlin.
Elphick, C., Meron, E. & Spiegel, E.A. (1988). Phys. Rev. Lett. 61, 496; Patterns of propagating pulses, Siam J. Appl. Math. , in press.
Elphick, C., Meron, E., Rinzel, J. & Spiegel, A. Impulse patterning and relaxational propagation in excitable media, submitted to J. Theor. Biol.
Dockery, J.D., Keener, J.P. & Tyson, J.J. (1988). Physica D (Amsterdam) 30, 177.
Pagola, A., Ross, J. & Vidal, C. (1980). J. Chem. Phys. 92, 163.
Winfree, A.T. (1987). When Time Breaks Down. Princeton University Press: New Jersey; Electrical Instability in Cardiac Muscle: phase singularities and rotors, J. Theor. Biol., in press.
Agladze, K.I., Panfilov, A.V. & Rudenko, A.N. (1988). Physica D (Amsterdam) 29, 409.
Meron, E. (1989). Phys. Rev. Lett. 63, 684.
Gardner-Medwin, A.R. (1972). J. Physiol. 222, 357.
Spear, J.F. & Moore, E.N. (1974). Circ. Res. 35, 782.
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© 1991 Springer Science+Business Media New York
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Meron, E. (1991). The Effect of Wavefront Interactions on Pattern Formation in Excitable Media. In: Holden, A.V., Markus, M., Othmer, H.G. (eds) Nonlinear Wave Processes in Excitable Media. NATO ASI Series, vol 244. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3683-7_15
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DOI: https://doi.org/10.1007/978-1-4899-3683-7_15
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