Dispersion relation for waves in the Belousov–Zhabotinsky reaction

Flesselles, Jean-Marc; Belmonte, Andrew; Gáspár, Vilmos

doi:10.1039/a707886b

Cited by 47 publications

(19 citation statements)

References 22 publications

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“…This type of dependence is commonly referred to as ''normal dispersion relation''. Furthermore, it was shown that in certain cases the velocity varies as the hyperbolic tangent of the normalized period of the wave train [4].…”

Section: Introductionmentioning

confidence: 99%

Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling

Bordyugov

Fischer

Engel

et al. 2010

Physica D: Nonlinear Phenomena

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Section: Introductionmentioning

confidence: 99%

Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling

Bordyugov

Fischer

Engel

et al. 2010

Physica D: Nonlinear Phenomena

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“…The Belousov-Zhabotinsky (BZ) reaction [2], which has been intensively studied as an easily controllable excitable medium, shows essentially normal dispersion [9]. This reaction involves the oxidation of an organic compound by bromate in acidic solution.…”

mentioning

confidence: 99%

Oscillatory Dispersion and Coexisting Stable Pulse Trains in an Excitable Medium

Bordiougov

Engel

2003

Phys. Rev. Lett.

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For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses. Crucial for the bistability is that the pulses in the trains are locked into one oscillation maximum in the tail of the preceding pulse in the train.

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“…However, the velocity decreases for decreasing wavelengths down to a critical value below which no propagation is possible. This most common form of the dispersion relation has been observed experimentally for various systems [16][17][18][19][20] and is therefore referred to as normal dispersion.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction

2001

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We report the formation of stable bound wave packets in a modified Belousov-Zhabotinsky reaction. These densely stacked structures arise from an attractive interaction between oxidation pulses that is not known from the classical Belousov-Zhabotinsky system. The characteristic stacking period increases with the initial concentration of bromate but decreases with cyclohexanedione. Wave stacking can also induce cascades of bunching events in which internally dense but mutually well segregated wave clusters are formed. For different initial concentrations, we observed the apparent merging of waves in front-to-back collisions. All three modes of wave dynamics are analyzed in terms of their dispersion behavior. The dispersion relations proved to be anomalous in each case and revealed the existence of an attractor which induces the formation of stable wave packets. The underlying mechanism has a pure reaction-diffusion character since wave propagation is not affected by fluid convection. At high initial concentrations of ferroin, we detected complex relaxation kinetics which indicate the presence of at least two independent species that control the recovery and hence the dispersion behavior of the medium.

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Dispersion relation for waves in the Belousov–Zhabotinsky reaction

Cited by 47 publications

References 22 publications

Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling

Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling

Oscillatory Dispersion and Coexisting Stable Pulse Trains in an Excitable Medium

Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov−Zhabotinsky Reaction

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