TY  - JOUR
A1  - Bordyugov, Grigory
A1  - Fischer, Nils
A1  - Engel, Harald
A1  - Manz, Niklas
A1  - Steinbock, Oliver
T1  - Anomalous dispersion in the Belousov-Zhabotinsky reaction : experiments and modeling
N2  - We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of "wave stacking", this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For "wave merging", wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, "wave tracking" is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.
Y1  - 2010
UR  - http://www.sciencedirect.com/science/journal/01672789
U6  - https://doi.org/10.1016/j.physd.2009.10.022
SN  - 0167-2789
ER  -