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通过周期性光照对图灵斑图的共振抑制

Resonant suppression of Turing patterns by periodic illumination.

作者信息

Dolnik M, Zhabotinsky A M, Epstein I R

机构信息

Department of Chemistry and Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02454-9110, USA.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Feb;63(2 Pt 2):026101. doi: 10.1103/PhysRevE.63.026101. Epub 2001 Jan 12.

Abstract

We study the resonant behavior of Turing pattern suppression in a model of the chlorine dioxide-iodine-malonic acid reaction with periodic illumination. The results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system. The resonance in Turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force. Square wave (on-off) periodic forcing is more effective in suppressing Turing patterns than sinusoidal forcing. We compare the dynamics of periodically forced Turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells. Bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns.

摘要

我们研究了在周期性光照下二氧化氯 - 碘 - 丙二酸反应模型中图灵模式抑制的共振行为。基于偏微分方程积分的模拟结果显示,在相应充分搅拌系统中的自激振荡频率处出现共振。图灵模式抑制中的共振在较低络合剂浓度下更尖锐,并且受到周期性驱动力波形的影响。方波(开 - 关)周期性强迫在抑制图灵模式方面比正弦强迫更有效。我们将周期性强迫图灵模式的动力学与两个相同耦合细胞系统中周期性强迫非均匀状态的动力学进行了比较。基于后一系统数值延拓的分岔分析对周期性强迫模式的主要共振区域边界给出了良好的预测。

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