31457
2010
2010
eng
article
1
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Hysteresis phenomenon in the dynamics of spiral waves rotating around a hole
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.
http://www.sciencedirect.com/science/journal/01672789
10.1016/j.physd.2009.07.018
0167-2789
allegro:1991-2014
10107743
Physica D : nonlinear phenomena. - ISSN 0167-2789. - 239 (2010), 11, S. 797 - 807
Vladimir Zykov
Grigory Bordyugov
Hartmut Lentz
Harald Engel
Institut für Physik und Astronomie
Referiert
32087
2010
2010
eng
article
1
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Anomalous dispersion in the Belousov-Zhabotinsky reaction : experiments and modeling
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.
http://www.sciencedirect.com/science/journal/01672789
10.1016/j.physd.2009.10.022
0167-2789
allegro:1991-2014
10108441
Physica D. - ISSN 0167-2789. - 239 (2010), 11, S. 766 - 775
Grigory Bordyugov
Nils Fischer
Harald Engel
Niklas Manz
Oliver Steinbock
Institut für Physik und Astronomie
Referiert
32088
2010
2010
eng
article
1
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Self-emerging and turbulent chimeras in oscillator chains
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.
http://pre.aps.org/
10.1103/Physreve.82.035205
1539-3755
allegro:1991-2014
10108442
Physical review E. - ISSN 1539-3755. - 82 (2010), 3, Art- 035205
Grigory Bordyugov
Arkady S. Pikovsky
Michael Rosenblum
Institut für Physik und Astronomie
Referiert