Dispersion of traveling waves in the Belousov-Zhabotinskii reaction

Abstract We use perturbation and numerical methods to calculate the dispersion relation for periodic wave train solutions of diffusion-reaction equations modeling the Belousov-Zhabotinskii reaction. These results are compared with experimental data for the Belousov-Zhabotinskii reagent and shown to be in good agreement.

[1]  Richard M. Noyes,et al.  Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction , 1974 .

[2]  John Rinzel Repetitive nerve impulse propagation: Numerical results and methods , 1977 .

[3]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[4]  J. Tyson,et al.  Target patterns in a realistic model of the Belousov–Zhabotinskii reaction , 1980 .

[5]  J. Rinzel,et al.  The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model. , 1981, Biophysical journal.

[6]  James P. Keener,et al.  Waves in Excitable Media , 1980 .

[7]  J. Tyson,et al.  The Speed of Propagation of Oxidizing and Reducing Wave Fronts in the Belousov-Zhabotinskii Reaction , 1984 .

[8]  John J. Tyson On Scaling the Oregonator Equations , 1981 .

[9]  J. L. Hudson,et al.  AN EXPERIMENTAL STUDY OF CHEMICAL WAVE PROPAGATION , 1973 .

[10]  J. Keener A geometrical theory for spiral waves in excitable media , 1986 .

[11]  R. J. Field,et al.  On the oxybromine chemistry rate constants with cerium ions in the Field-Koeroes-Noyes mechanism of the Belousov-Zhabotinskii reaction: the equilibrium HBrO2 + BrO3- + H+ .dblharw. 2BrO.ovrhdot.2 + H2O , 1986 .

[12]  L. Kuhnert,et al.  Velocity of trigger waves and temperature dependence of autowave processes in the Belousov-Zhabotinsky reaction , 1985 .

[13]  J. Keener,et al.  Spiral waves in the Belousov-Zhabotinskii reaction , 1986 .

[14]  J Rinzel,et al.  Traveling wave solutions of a nerve conduction equation. , 1973, Biophysical journal.

[15]  Measurement of dispersion relation of chemical waves in an oscillatory reacting medium , 1988 .

[16]  R. G. Casten,et al.  Perturbation analysis of an approximation to the Hodgkin-Huxley theory , 1975 .

[17]  K. Showalter Trigger waves in the acidic bromate oxidation of ferroin , 1981 .

[18]  A. Winfree Spiral Waves of Chemical Activity , 1972, Science.