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Weimar, Jörg R.; Tyson, John J.; Watson, Layne T.

Third generation cellular automaton for modeling excitable media. (English) Zbl 0744.92003

Physica D 55, No. 3-4, 328-339 (1992).
Summary: This paper introduces a new cellular automaton model of excitable media with improved treatments of (1) diffusion and wave propagation, and (2) slow dynamics of the recovery variable. The automaton is both computationally efficient and faithful to the underlying partial differential equations.

Cited in 8 Documents

MSC:

92B05 General biology and biomathematics
92-08 Computational methods for problems pertaining to biology
65Z05 Applications to the sciences

Keywords:

Oregonator model; new cellular automaton model of excitable media; diffusion; wave propagation; slow dynamics of the recovery variable
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References:

[1] Courtemanche, M.; Skaggs, W.; Winfree, A. T., Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model, Physica D, 41, 173-182 (1990) · Zbl 0711.35068
[2] Fast, V. G.; Efimov, I. G., Stability of vortex rotation in an excitable cellular medium, Physica D, 49, 75-81 (1991)
[3] Field, R. J.; Noyes, R. M., Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction, J. Chem. Phys., 60, 1877-1884 (1974)
[4] FitzHugh, R., Impulse and physiological states in models of nerve membrane, Biophysics J., 1, 445-466 (1961)
[5] Gerhardt, M.; Schuster, H.; Tyson, J. J., A cellular automaton model of excitable media. II. Curvature, dispersion, rotating waves and meandering waves, Physica D, 46, 392-415 (1990) · Zbl 0800.92028
[6] Gerhardt, M.; Schuster, H.; Tyson, J. J., A cellular automaton model of excitable media. III. Fitting the Belousov-Zhabotinsky reaction, Physica D, 46, 416-425 (1990) · Zbl 0800.92029
[7] Gerhardt, M.; Schuster, H.; Tyson, J. J., A cellular automaton model of excitable media including curvature and dispersion, Science, 247, 1563-1566 (1990) · Zbl 1226.37004
[8] Greenberg, J. M.; Hassard, B. D.; Hastings, S. P., Pattern formation and periodic structures in systems modeled by reaction-diffusion equations, Bull. Am. Math. Soc., 84, 1296-1327 (1978) · Zbl 0424.35011
[9] Greenberg, J. M.; Hastings, S. P., Spatial patterns for discrete models of diffusion in excitable media, SIAM J. Appl. Math., 34, 515-523 (1987) · Zbl 0398.92004
[10] Jahnke, W.; Skaggs, W. E.; Winfree, A. T., Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the two-variable Oregonator model, J. Phys. Chem., 93, 740-749 (1989)
[11] Jahnke, W.; Winfree, A. T., A survey of spiral wave behaviors in the Oregonator model, Intern. J. Bifurcations Chaos, 1, 445-466 (1991) · Zbl 0900.92066
[12] M. Markus, Dynamics of a cellular automaton with randomly distributed elements, in: Mathematical Population Dynamics: Proc. Second Intern. Conf. (Dekker, New York) in press.; M. Markus, Dynamics of a cellular automaton with randomly distributed elements, in: Mathematical Population Dynamics: Proc. Second Intern. Conf. (Dekker, New York) in press.
[13] Markus, M.; Hess, B., Isotropic cellular automaton for modeling excitable media, Nature, 347, 56-58 (1990)
[14] Moe, G. K.; Rheinboldt, W. C.; Abildskov, J. A., A computer model of atrial fibrillation, Am. Heart J., 67, 200-220 (1964)
[15] Tyson, J. J., A quantitative account of oscillations, bistability, and traveling waves in the Belousov-Zhabotinsky reaction, (Field, R. J.; Burger, M., Oscillations and Traveling Waves in Chemical Systems (1985), Wiley: Wiley New York), 93-144
[16] Tyson, J. J.; Keener, J. P., Singular perturbation theory of traveling waves in excitable media (A review), Physica D, 32, 327-361 (1988) · Zbl 0656.76018
[17] Tyson, J. J.; Manoranjan, V. S., The speed of propagation of oxidizing and reducing wave fronts in the Belousov-Zhabotinsky reaction, (Vidal, C.; Pacault, A., Non-Equilibrium Dynamics in Chemical Systems (1984), Springer: Springer Berlin), 89-93
[18] Weimar, J. R.; Tyson, J. J.; Watson, L. T., Diffusion and wave propagation in cellular automaton models of excitable media, Physica D, 55, 307-325 (1991)
[19] Wiener, N.; Rosenblueth, A., The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. Mexico, 16, 205-265 (1946) · Zbl 0134.37904
[20] Winfree, A. T., Spiral waves of chemical activity, Science, 175, 634-636 (1972)
[21] Winfree, A. T., When time breaks down (1987), Princeton Univ. Press: Princeton Univ. Press Princeton
[22] Zhabotinsky, A. M.; Zaikin, A. N., Concentration wave propagation in two-dimensional liquid-phase self-oscillating system, Nature, 225, 535-537 (1970)
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