席尔宾斯基络分析与同步.pdf

河北工业大学硕士学位论文
席尔宾斯基网络分析与同步

摘要
在现实世界中,有一大类系统例如城市道路系统、人际交往系统和生物系统等都可以
用著名的席尔宾斯基分形垫映射成的不相容网络——席尔宾斯基网络进行描述。所以,对
席尔宾斯基网络进行分析及其同步的研究对了解和认识现实系统意义重大。
本文主要工作如下:
第一部分:分析研究了席尔宾斯基网络。特别是对席尔宾斯基 SG3 () t 网络的度分布,
平均路径长度和聚类系数三个主要特征参量分别通过解析计算和数值模拟两方面进行了
分析研究。
第二部分:席尔宾斯基 SG3 () t 动态网络同步的研究。特别是对以 Lorenz 混沌系统为节
点的席尔宾斯基动态网络,分析了其第一个迭代步的同步性能,并分别就其第一和第二迭
代步时的同步进行了数值模拟实验,且对模拟结果给出了分析。
第三部分:通过随机连接方法改进了席尔宾斯基 SG3 (2) 动态网络的同步能力。提出了
随机加边模型和随机重连模型,数值模拟其同步发现随机连接确实能提高该网络的同步性
能
第四部分:以混沌态的 Lorenz 系统作为网络节点,以节点间单变量线性耦合方法模拟
实现三种结构不同的席尔宾斯基网络同步。
关键词:席尔宾斯基网络,席尔宾斯基动态网络同步,耦合,随机连接








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席尔宾斯基网络分析与同步
ANALYSIS OF WORKS AND ITS
SYNCHRONIZATION

ABSTRACT

works—works, which are induced by the famous Sierpinski
fractals, can describe a large class of systems in real life ,for example in the road system of city,
munication system, biological systems and so on. So it is significant to analyze
works and study on its synchronization.
The fundamental works of this paper are summarized as follows:
In part one, we will analyze and study works. Especially, we will analyze and
study degree correlations, average path length and clustering coefficient of Sierpinski SG3 () t
networks by analytical calculation and numerical simulation.
In part two, we will study the synchronization of Sierpinski SG3 () t works.
Especially, we will analysis synchronization performance of Sierpinski works at first
step, which is added chaotic Lorenz system on nodes. Then it is respectively to simulate
synchronization of Sierpinski works at first step and second step. Finally, it is to
analysis its simulation results.
In part three, we will improve synchronization performance of Sierpinski work
SG3 (2) by the method of random connection. We present one model with random inserting side
into SG3 (2) network and the other model with random reconnecting sides of SG3 (2)
it is to simulate their synchronization. Finally, we obtain that syn