TY  - JOUR
A1  - Zykov, Vladimir
A1  - Bordyugov, Grigory
A1  - Lentz, Hartmut
A1  - Engel, Harald
T1  - Hysteresis phenomenon in the dynamics of spiral waves rotating around a hole
N2  - Hysteresis in the pinning-depinning transitions of spiral waves rotating around a hole in a circular shaped two- dimensional excitable medium is studied both by use of the continuation software AUTO and by direct numerical integration of the reaction-diffusion equations for the FitzHugh-Nagumo model. In order to clarify the role of different factors in this phenomenon, a kinematical description is applied. It is found that the hysteresis phenomenon computed for the reaction-diffusion model can be reproduced qualitatively only when a nonlinear eikonal equation (i.e. velocity- curvature relationship) is assumed. However, to obtain quantitative agreement, the dispersion relation has to be taken into account.
Y1  - 2010
UR  - http://www.sciencedirect.com/science/journal/01672789
U6  - https://doi.org/10.1016/j.physd.2009.07.018
SN  - 0167-2789
ER  - 
TY  - JOUR
A1  - Bordyugov, Grigory
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Self-emerging and turbulent chimeras in oscillator chains
N2  - We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e., a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state. We develop a theory of chimera based on the Ott-Antonsen equations for the local complex order parameter. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.82.035205
SN  - 1539-3755
ER  - 
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  -