Topaz Chad M, Catllá Anne J
Department of Mathematics, Statistics, and Computer Science, Macalester College, St. Paul, Minnesota 55105, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Feb;81(2 Pt 2):026213. doi: 10.1103/PhysRevE.81.026213. Epub 2010 Feb 26.
We study time-periodic forcing of spatially extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results are consistent with features of previous experiments on the chlorine dioxide-iodine-malonic acid chemical reaction. However, we also find examples of the enhancing case, which has not yet been observed in experiment. Numerical simulations verify the predicted dependence on the forcing parameters.
我们研究了图灵 - 霍普夫分岔点附近空间扩展模式的时间周期强迫。基于对称性的范式分析得出了几个预测结果，包括：（i）在固有霍普夫频率附近的弱强迫会使图灵振幅增强或抑制，其增强或抑制的量与强迫强度呈二次方比例关系；（ii）对于偏离霍普夫频率的强迫，会观察到最强的效应。为了将我们的结果应用于特定模型，我们对一般的双组分反应扩散系统进行了微扰分析，这揭示了强迫是抑制还是增强空间模式。对于抑制情况，我们的结果与先前关于二氧化氯 - 碘 - 丙二酸化学反应实验的特征一致。然而，我们也发现了增强情况的例子，这在实验中尚未被观察到。数值模拟验证了所预测的对强迫参数的依赖性。
