频率分布非对称下的爆发式同步
发布时间：2018-11-15 17:38
【摘要】：爆发式同步现象指的是复杂网络上的振子,随着耦合强度的增加,从混乱状态开始,经历一个不连续的、伴随着磁滞区的一级相变,变化到同步状态的过程。自2011年西班牙小组发表了 Kuramoto模型在Scale-Free网上的爆发式同步以来,该领域迅速成为了热点,得到了广泛的关注。随后胡鑫、张希昀等人,在前人的基础上提出了以振子本征频率作为耦合权重的新的广义Kuramoto模型,取得了一系列的研究成果。考虑到简化理论计算等原因,之前所研究的频率权重模型,其本征频率都取为对称的分布,而频率分布非对称的情形并未得到研究。从这一点出发,本文研究了频率权重模型在典型的非对称频率分布下的同步化行为。通过数值模拟和理论分析,我们得到了以下主要结果:1.在多种非对称频率分布下,频率权重Kuramoto模型都能表现出爆发式同步现象,并且随着系统非对称性的增强,系统会由一级相变逐步过渡到二级相变;2.在非对称洛伦兹分布和非对称三角分布中,发现并刻画了一类新的协同态,即具有阵发特性的Bellarophon态。本文的结果能帮助我们更加全面地理解耦合相振子系统中的爆发式同步。
[Abstract]:The explosive synchronization phenomenon refers to the oscillator in a complex network. With the increase of coupling intensity, it goes through a discontinuous first order phase transition along with the hysteresis region and changes to the synchronous state with the increase of the coupling strength. Since the Spanish team published the explosive synchronization of the Kuramoto model on Scale-Free in 2011, the field has quickly become a hot spot and received wide attention. Subsequently, Hu Xin, Zhang Xiyun and others put forward a new generalized Kuramoto model with the eigenfrequency of oscillator as coupling weight on the basis of predecessors, and obtained a series of research results. Considering the simplified theoretical calculation and other reasons, the eigenfrequencies of the previously studied frequency weighting model are all symmetric distribution, but the asymmetric frequency distribution is not studied. From this point of view, the synchronization behavior of the frequency weight model under the typical asymmetric frequency distribution is studied. By numerical simulation and theoretical analysis, we get the following main results: 1. Under a variety of asymmetric frequency distributions, the frequency weighted Kuramoto model can exhibit explosive synchronization phenomenon, and with the increase of the system asymmetry, the system will gradually transition from the first-order phase transition to the second-order phase transition; 2. In the asymmetric Lorentz distribution and the asymmetric triangular distribution, we find and characterize a new class of cooperative states, that is, the Bellarophon states with the property of matrix. The results in this paper can help us to understand the burst synchronization in the coupled phase oscillator system more comprehensively.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
本文编号：2333986
[Abstract]:The explosive synchronization phenomenon refers to the oscillator in a complex network. With the increase of coupling intensity, it goes through a discontinuous first order phase transition along with the hysteresis region and changes to the synchronous state with the increase of the coupling strength. Since the Spanish team published the explosive synchronization of the Kuramoto model on Scale-Free in 2011, the field has quickly become a hot spot and received wide attention. Subsequently, Hu Xin, Zhang Xiyun and others put forward a new generalized Kuramoto model with the eigenfrequency of oscillator as coupling weight on the basis of predecessors, and obtained a series of research results. Considering the simplified theoretical calculation and other reasons, the eigenfrequencies of the previously studied frequency weighting model are all symmetric distribution, but the asymmetric frequency distribution is not studied. From this point of view, the synchronization behavior of the frequency weight model under the typical asymmetric frequency distribution is studied. By numerical simulation and theoretical analysis, we get the following main results: 1. Under a variety of asymmetric frequency distributions, the frequency weighted Kuramoto model can exhibit explosive synchronization phenomenon, and with the increase of the system asymmetry, the system will gradually transition from the first-order phase transition to the second-order phase transition; 2. In the asymmetric Lorentz distribution and the asymmetric triangular distribution, we find and characterize a new class of cooperative states, that is, the Bellarophon states with the property of matrix. The results in this paper can help us to understand the burst synchronization in the coupled phase oscillator system more comprehensively.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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