Pei X, Moss F
Department of Physics and Astronomy, University of Missouri at St Louis 63121, USA.
Nature. 1996 Feb 15;379(6566):618-21. doi: 10.1038/379618a0.
Attempts to detect and characterize chaos in biological systems are of considerable interest, especially in medical science, where successful demonstrations may lead to new diagnostic tools and therapies. Unfortunately, conventional methods for identifying chaos often yield equivocal results when applied to biological data, which are usually heavily contaminated with noise. For such applications, a new technique based on the detection of unstable periodic orbits holds promise. Infinite sets of unstable periodic orbits underlie chaos in dissipative systems; accordingly, the new method searches a time series only for rare events characteristic of these unstable orbits, rather than analysing the structure of the series as a whole. Here we demonstrate the efficacy of the method when applied to the dynamics of the crayfish caudal photoreceptor (subject to stimuli representative of the animal's natural habitat). Our findings confirm the existence of low-dimensional dynamics in the system, and strongly suggest the existence of deterministic chaos. More importantly, these results demonstrate the power of methods based on the detection of unstable periodic orbits for identifying low-dimensional dynamics--and, in particular, chaos--in biological systems.
检测和描述生物系统中的混沌现象极具意义，尤其在医学领域，成功的论证可能会带来新的诊断工具和治疗方法。不幸的是，传统的混沌识别方法应用于生物数据时，往往会得出模棱两可的结果，因为生物数据通常被大量噪声严重污染。对于此类应用，一种基于检测不稳定周期轨道的新技术有望解决问题。在耗散系统中，混沌现象的背后存在着无穷多组不稳定周期轨道；因此，新方法仅在时间序列中搜索这些不稳定轨道所特有的罕见事件，而非分析整个序列的结构。在此，我们展示了该方法应用于小龙虾尾感光器动力学（受代表动物自然栖息地的刺激）时的有效性。我们的研究结果证实了该系统中存在低维动力学，并有力地表明了确定性混沌的存在。更重要的是，这些结果证明了基于检测不稳定周期轨道的方法在识别生物系统中的低维动力学——尤其是混沌现象——方面的强大作用。
