论文标题
复杂性定量中的非线性动力学
Nonlinear Dynamics in Complexity Quantification
论文作者
论文摘要
由于非线性引起的混乱系统在当前的世界和混乱模型中引起了人们的关注。多种操作条件的系统几乎都将其应用于工程和科学的所有分支。在混乱的研究和非线性的历史中,可以区分许多不同但共存的阶段[1]。在初始阶段,混乱被认为是确定性的制度,很可能是导致被视为噪声的变化,因此被建模为随机过程。在第二阶段,建立用于检测混乱动力学的标准,从而建立在量化混乱所必需的动态不变的标准是很重要的。第三步是开发机器学习模型,这些模型可以从奇怪的吸引子的数据中学习动态和混乱[2]。关于这一方面,开发了各种模型结构,并研究了它们从给定数据集中检测混乱的能力[3]。这些模型结构包括径向基函数,以及局部线性映射等。目前正在研究第三阶段,以及围绕非线性动态和混乱的其他问题,例如降低和控制等问题。
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science. In the history of chaotic studies and nonlinearity, many different but co-existent phases can be distinguished [1]. In the initial phase, chaos was considered as a deterministic regime which, most probably, was responsible for the variations that was regarded as noise and thus was being modeled as a stochastic process. In the second phase, it was of great significance to establish criteria for detecting chaotic dynamics and thus establishing dynamical invariants which were necessary in quantifying chaos. The third step which was to develop machine learning models which could learn the dynamics and chaos from the data of the strange attractor [2]. With respect to this aspect, various model structures were developed and investigated on their ability to detect chaos from a given set of data [3]. These model structures included radial basis functions, and local linear mapping among others. The third phase is currently being investigated together with other issues surrounding nonlinear dynamics and chaos, for instance in noise reduction and control, among other issues.