摘要翻译：
对于大的耦合非线性系统，高维相空间的可视化是很困难的，这在小系统中已经得到了深入的研究，如千疮百孔的盆地等现象。本文提出了一种通过定义相空间截面来缩小相空间的方法。该方法应用于由Ito和Kaneko提出的动态耦合映射系统(Phys.Rev.Lett.，88，028701，2001&Phys.Rev.E，67，046226，2003)。我们证明了不同同步行为的相位之间的过渡并不总是尖锐的，而是可以在相位空间和参数空间中用分形边界来表征。
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英文标题：
《Using a phase space cross section to study large complex systems》
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作者：
Gil Benk\"o and Henrik Jeldtoft Jensen
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Mathematics        数学
二级分类：Dynamical Systems        动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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英文摘要：
  For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce the phase space by defining a phase space cross section. The method is applied to a system of dynamically coupled maps introduced by Ito & Kaneko (Phys. Rev. Lett., 88, 028701, 2001 & Phys. Rev. E, 67, 046226, 2003). We show that the transitions between phases of different synchronization behaviour are not always sharp but can be characterized by fractal boundaries in both phase and parameter space.
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PDF链接：
https://arxiv.org/pdf/707.1439