利用回复性分析对复杂系统同步的研究

发布时间：2018-05-11 19:37

本文选题：复杂系统 + 复杂网络　；参考：《河北师范大学》2017年硕士论文

【摘要】：复杂系统是复杂性科学的主要研究对象,复杂系统的同步现象是目前的一个研究热点。在研究复杂系统时,复杂网络被看作一个重要的数学模型,其相关理论对于复杂系统研究具有重要意义。回复性是动力系统的一个基本性质,常用来描述相空间系统的动力学行为。递归图(RP)是基于回复性的可视化工具,回复性量化分析(RQA)是对回复性进行定量分析的度量。递归图(RP)和回复性量化分析(RQA)作为研究复杂系统的一种新方法,被广泛应用到复杂系统的众多问题中。本文利用递归图(RP)和回复性量化分析(RQA)方法探讨了复杂系统同步与回复性之间的关系,叙述了递归图(RP)检测复杂系统广义同步和相同步的一般方法,并利用回复网络的相关特征量分析三个系统相互耦合问题。本文的主要工作包括:1、定义一个新的特征量用来检测复杂系统的相同步,利用递归图(RP)和回复性量化分析(RQA)检测系统的广义同步和相同步,并通过对参数不匹配的7)0)驱动响应系统进行数值模拟,验证了在一定条件下广义同步于相同步的关系。2、定义了三个系统之间的交叉传递性和全局交叉聚类系数,给出利用这两个特征量分析了三个耦合系统的同步问题,并通过对三个单向耦合的Rossler系统和环式单向耦合的三个Lorenz系统进行数值模拟,验证了利用交叉传递性和全局交叉聚类系数分析三个耦合系统同步的可行性。
[Abstract]:Complex system is the main research object of complexity science. Synchronization of complex system is a hot research topic at present. In the study of complex systems, complex networks are regarded as an important mathematical model, and the relevant theories are of great significance to the study of complex systems. Reversibility is a basic property of dynamic systems, which is often used to describe the dynamic behavior of phase space systems. Recursive graph (RP) is a visual tool based on reversibility, and RQA is a measure of quantitative analysis of reversibility. As a new method to study complex systems, recursive graph (RP) and reversibility quantization analysis (RQA) have been widely used in many problems of complex systems. In this paper, the relationship between synchronization and reversibility of complex systems is discussed by means of recursive graph (RP) and reversibility quantitative analysis (RQA), and the general method of detecting generalized synchronization and phase synchronization of complex systems by recursive graph (RP) is described. The coupling problem of the three systems is analyzed by using the correlation characteristic of the reverse-network. The main work of this paper includes: 1. A new feature is defined to detect phase synchronization of complex systems. The generalized synchronization and phase synchronization are detected by recursive graph (RP) and reversibility quantization analysis (RQA). Through numerical simulation of 7 / 0) drive response system with mismatched parameters, the relationship between generalized synchronization and phase synchronization is verified under certain conditions. The cross transitivity and global cross clustering coefficient of the three systems are defined. The synchronization problem of the three coupling systems is analyzed by using these two eigenvalues, and the numerical simulation of the three unidirectional coupling Rossler systems and the loop unidirectional coupling three Lorenz systems is carried out. The feasibility of using cross transitivity and global cross clustering coefficient to analyze the synchronization of three coupled systems is verified.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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