Complex Systems: Phenomenology, Modeling, Analysis
Complex Systems: Phenomenology, Modeling, Analysis
复制标题
复杂系统：现象学、建模、分析
DOI：
10.15344/2456-8155/2016/105
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Iliopoulos
中科院分区：
文献类型：
--
作者：
A. Iliopoulos
本文简要概述了复杂系统及其基本特征，以及为其分析而开发的模型和数学工具。本综述是根据作者的相关经验、活动和科学兴趣而形成的，即主要关注非线性时间序列分析和统计及其在不同物理系统中的应用。特别是，给出了关于复杂系统现象学的粗略轮廓，例如远离平衡热力学和 Tsallis 统计、幂律标度、多重分形、低维混沌、SOC、奇怪的动力学、反常扩散和湍流间歇性。此外，还简要描述了基于方程或基于代理的模型的不完整列表，例如Kuramoto – Sivashinsky方程、三次复数Ginzburg-Landau方程、反应扩散方程、分数方程、元胞自动机、复杂网络和人工神经网络。对非线性时间序列分析复杂系统进行了更广泛的回顾，描述了重构相空间中的互信息、平坦系数、结构函数、Tsallis q-三元组、相关维数和 Lyapunov 指数等工具，可以为复杂系统的动力学提供有价值的信息。最后，提供了非线性时间序列分析在地震、地球磁层、太阳等离子体和太阳风、材料塑性变形、癫痫、经济指标和DNA结构等各种物理系统中的应用。
In this paper a short overview on complex systems and their basic features, as well as the models and mathematical tools developed for their analysis, is given. This review is formed according to the related experience, activity and scientific interests of the author, namely focused on mainly in nonlinear time series analysis and statistics and their applications on different physical systems. In particular, rough outlines are given concerning the phenomenology of complex systems, e.g. far from equilibrium thermodynamics and Tsallis statistics, power law scaling, multi-fractality, low dimensional chaos, SOC, strange kinetics and anomalous diffusion and turbulent intermittency. In addition, a non-complete list of models, based on equations or agent based, is briefly described such as Kuramoto – Sivashinsky equation, cubic complex Ginzburg-Landau Equation, reaction-diffusion Equation, fractional equations, cellular automata, complex networks and artificial neural networks. A more extended review is provided concerning the nonlinear time series analysis complex systems, describing tools like mutual information, flatness coefficient, structure functions, Tsallis q-triplet, correlation dimension and Lyapunov exponents in the reconstructed phase space, which can provide valuable information for the complex system’s dynamics. Finally, applications of nonlinear time series analysis on various physical systems, such as earthquakes, Earth’s magnetosphere, solar plasma and solar wind, plastic deformation of materials, epilepsy, economical indices and DNA structure, are provided.