Marts Bradley, Hagberg Aric, Meron Ehud, Lin Anna L
Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Chaos. 2006 Sep;16(3):037113. doi: 10.1063/1.2346153.
Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.
空间扩展系统中的均匀振荡与单个受迫振荡器的阿诺德舌区内的时间周期强迫发生共振。阿诺德舌区是由强迫振幅和频率所跨越的参数空间中的楔形区域，在该区域内振荡器的频率被锁定为强迫频率的一部分。空间图案化可以改变这些区域。我们在此描述两种影响在强迫频率一半处频率锁定的图案形成机制。这些机制与相前沿不稳定性以及静止状态的类图灵不稳定性相关。我们的研究结合了对由周期性光照强迫的钌催化光敏贝洛索夫 - 扎博廷斯基反应的实验，以及两个模型系统（菲茨休 - 纳古莫模型和复金兹堡 - 朗道方程）的数值和分析研究，其中包含描述周期性强迫的附加项。
