Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I, Engel H
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016214. doi: 10.1103/PhysRevE.68.016214. Epub 2003 Jul 16.
It is shown that meandering spiral waves rotating in excitable media subjected to periodic external forcing or feedback control resemble many features of nonlinear lumped oscillators. In particular, the period shift function obtained for the Poincaré oscillator is qualitatively identical to that for spiral waves under fixed phase control. On the other hand, under one-channel feedback control, meandering spiral waves exhibit quite different dynamic regimes appearing as specific features of a distributed system. In particular, three types of attractors (resonance, entrainment, and asynchronous) of spiral waves are observed in experiments with the light-sensitive Belousov-Zhabotinsky reaction and in numerical simulations performed for the underlying Oregonator model. A theory of the resonance attractor for meandering spiral waves is developed which predicts the attractor radius and specifies the basins of attraction in good quantitative agreement with the numerical computations and experimental observations.
结果表明，在受到周期性外部强迫或反馈控制的可激发介质中旋转的蜿蜒螺旋波，类似于非线性集总振荡器的许多特征。特别是，庞加莱振荡器的周期移位函数在定性上与固定相位控制下螺旋波的周期移位函数相同。另一方面，在单通道反馈控制下，蜿蜒螺旋波表现出截然不同的动力学状态，呈现为分布式系统的特定特征。特别是，在对光敏贝洛索夫-扎博廷斯基反应进行的实验以及对基础俄勒冈振子模型进行的数值模拟中，观察到了螺旋波的三种吸引子（共振、同步和异步）。针对蜿蜒螺旋波的共振吸引子发展了一种理论，该理论预测了吸引子半径，并在定量上与数值计算和实验观测结果很好地吻合，确定了吸引域。
