Li Wei-Shen, Hu Wen-Yong, Pang Ya-Chun, Liu Tai-Ran, Zhong Wei-Rong, Shao Yuan-Zhi
School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066132. doi: 10.1103/PhysRevE.85.066132. Epub 2012 Jun 28.
A chlorine-iodine-malonic-acid Turing system involving a local concentration-dependent diffusivity (LCDD) has fundamental significance for physical, chemical, and biological systems with inhomogeneous medium. We investigated such a system by both numerical computation and mathematical analysis. Our research reveals that a variable local diffusivity has an evident effect on regulating the Turing patterns for different modes. An intrinsic square-root law is given by λ ∼ (c(1)+c(2)k)(1/2), which relates the pattern wavelength (λ) with the LCDD coefficient (k). This law indicates that the system pattern has the properties of an equivalent Turing pattern. The current study confirms that, for the Turing system with LCDD, the system pattern form retains the basic characteristics of a traditional Turing pattern in a wide range of LCDD coefficients.
一个涉及局部浓度依赖扩散率（LCDD）的氯 - 碘 - 丙二酸图灵系统对于具有非均匀介质的物理、化学和生物系统具有重要意义。我们通过数值计算和数学分析对这样一个系统进行了研究。我们的研究表明，可变的局部扩散率对不同模式的图灵模式调节有明显影响。给出了一个内在的平方根定律λ ∼ (c(1)+c(2)k)(1/2)，它将模式波长（λ）与LCDD系数（k）联系起来。该定律表明系统模式具有等效图灵模式的性质。当前研究证实，对于具有LCDD的图灵系统，在广泛的LCDD系数范围内，系统模式形式保留了传统图灵模式的基本特征。
