Winfree A T
Department of Ecology and Evolutionary Biology, University of Arizona, Tucson 85721.
Nature. 1994 Sep 15;371(6494):233-6. doi: 10.1038/371233a0.
Excitable media are exemplified by a range of living systems, such as mammalian heart muscle and its cells and Xenopus eggs. They also occur in non-living systems such as the autocatalytic Belousov-Zhabotinsky reaction. In most of these systems, activity patterns, such as concentration waves, typically radiate as spiral waves from a vortex of excitation created by some nonuniform stimulus. In three-dimensional systems, the vortex is commonly a line, and these vortex lines can form linked and knotted rings which contract into compact, particle-like bundles. In most previous work these stable 'organizing centres' have been found to be symmetrical and can be classified topologically. Here I show through numerical studies of a generic excitable medium that the more general configuration of vortex lines is a turbulent tangle, which is robust against changes in the parameters of the system or perturbations to it. In view of their stability, I suggest that these turbulent tangles should be observable in any of the many known excitable media.
可兴奋介质的例子包括一系列生命系统，如哺乳动物的心肌及其细胞以及非洲爪蟾卵。它们也存在于非生命系统中，如自催化的贝洛索夫-扎博廷斯基反应。在大多数这些系统中，诸如浓度波之类的活动模式通常从由某种不均匀刺激产生的激发涡旋以螺旋波的形式辐射。在三维系统中，涡旋通常是一条线，并且这些涡旋线可以形成相连和打结的环，这些环会收缩成紧凑的、类似粒子的束。在大多数先前的工作中，这些稳定的“组织中心”被发现是对称的，并且可以进行拓扑分类。在这里，我通过对一种通用可兴奋介质的数值研究表明，涡旋线更普遍的构型是一种湍流缠结，它对系统参数的变化或对其的扰动具有鲁棒性。鉴于它们的稳定性，我认为这些湍流缠结在许多已知的可兴奋介质中的任何一种中都应该是可观测的。
