Hu Hai Xiang, Li Qian Shu, Ji Lin
Institute of Chemical Physics, Beijing Institute of Technology, China.
Phys Chem Chem Phys. 2008 Jan 21;10(3):438-41. doi: 10.1039/b712567d. Epub 2007 Nov 9.
Various oscillatory superlattice patterns in a reaction-diffusion system are observed by means of delay feedback (DF) in the parametric domain where the system without DF displays uniform bulk oscillation. By varying DF parameters within an appropriate range, the system undergoes transitions to oscillatory hexagons, stripes and squares, and square superlattices with different wavenumbers are also obtained. Linear stability analysis reveals that the patterns do not result from the Turing instability and a possible mechanism of pattern formation is suggested and proved analytically: DF induces instability of a homogeneous limit cycle with respect to spatial perturbations even if the Turing instability does not occur, so that oscillatory patterns possessing the corresponding spatial modes are produced. The different behavior of the dominant characteristic multiplier seems to be connected to the pattern selection. Here it is clearly demonstrated that DF can play a destabilizing role in spatially extended system instead of stabilizing the periodic orbits or turbulent states, which most earlier works have usually focused on.
在一个反应扩散系统中，通过延迟反馈（DF）在参数域中观察到各种振荡超晶格模式，在该参数域中，没有DF的系统表现出均匀的整体振荡。通过在适当范围内改变DF参数，系统会转变为振荡六边形、条纹和正方形，并且还获得了具有不同波数的正方形超晶格。线性稳定性分析表明，这些模式并非由图灵不稳定性产生，并且提出并通过解析证明了一种可能的模式形成机制：即使图灵不稳定性不发生，DF也会导致均匀极限环相对于空间扰动的不稳定性，从而产生具有相应空间模式的振荡模式。主导特征乘数的不同行为似乎与模式选择有关。这里清楚地表明，DF在空间扩展系统中可以起到破坏稳定的作用，而不是像大多数早期工作通常关注的那样稳定周期轨道或湍流状态。
