Zemskov Evgeny P, Vanag Vladimir K, Epstein Irving R
Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 2):036216. doi: 10.1103/PhysRevE.84.036216. Epub 2011 Sep 26.
Using Taylor series expansion, multiscaling, and further expansion in powers of a small parameter, we develop general amplitude equations for two-variable reaction-diffusion systems with cross-diffusion terms in the cases of Hopf and Turing instabilities. We apply this analysis to the Oregonator and Brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices. Our analysis facilitates finding regions of supercritical and subcritical bifurcations, as well as wave and antiwave domains and domains of turbulent waves in the case of Hopf instability.
利用泰勒级数展开、多尺度分析以及在小参数幂次上的进一步展开，我们针对具有交叉扩散项的双变量反应扩散系统，在霍普夫（Hopf）和图灵（Turing）不稳定性情形下，推导出了一般振幅方程。我们将此分析应用于俄勒冈振子（Oregonator）模型和布鲁塞尔振子（Brusselator）模型，发现由于它们群落矩阵结构不同，在这两个模型中，由激活剂引起的抑制剂交叉扩散和由抑制剂引起的激活剂交叉扩散具有相反的效应。我们的分析有助于找到超临界和亚临界分岔区域，以及在霍普夫不稳定性情形下的波域、反波域和湍流波域。
