兰州大学机构库 >物理科学与技术学院
时滞系统与复杂动力学网络的研究
Alternative TitleExploring dynamics of time-delay systems and complex networks
祁伟
Thesis Advisor汪映海
2009-05-22
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword时滞系统 复杂动力学网络 混沌控制 同步性 一致性
Abstract本文对时滞系统和复杂网络的动力学进行了研究,涉及时滞系统的混沌控制、复杂动态网络系统的同步与控制、复杂网络中的一致性问题。主要工作如下: 1.将多时滞反馈控制方法运用于非线性时滞系统。结果发现,这种方法对长时滞区域的超混沌、中时滞和短时滞区域的混沌都实现了有效地控制,从而将此方法推广到无穷维系统。 2.混沌系统相互耦合时的时滞效应有助于系统之间的同步,该文 研究了节点含时滞的混沌系统在时滞耦合的小世界网络上的同步问题,考虑了耦合时滞相同和满足高斯分布两种情形。结果表明,只要网络的耦合强度和耦合时滞的值足够大,耦合时滞有助于提高网络的同步性能。 3.根据多时滞反馈控制方法设计了一种线性反馈控制器,研究了无标度网络上节点动力学系统分别是Chua's混沌系统、Baier-Sahle超混沌系统、无穷维的Ikeda时滞系统的控制问题,结果很好地验证了这种方法对于无标度网络上的混沌行为实现牵制控制的有效性。 4.采用BA模型,根据其度值存在的次序关系选择网络中每条连接的权值,研究了不对称加权方法对网络的一致性有很大的影响。结果发现当度值较大的节点驱动度值较小的节点的耦合占主导时,整个网络达到全局一致性的收敛速度和对延迟时间的鲁棒性两个方面都有了提高。
Other AbstractIn this thesis, we did some deep and detailed studies on dynamics on time-delay systems and complex networks. Our work contains chaos control of time-delay systems, synchronization and pinning control on complex dynamical networks, and consensus problems of multi-agent systems. Firstly, We discuss the stabilization problem in the infinite-dimensional time-delay systems with MDFC. Studies show that MDFC works well for stabilizing (unstable) steady states in all delay regions.So this work is mainly devoted to extending MDFC to infinite-dimensional time-delayed systems. Secondly, Coupling delays can be conducive to synchronization of coupled chaotic maps. We study synchronization of time-delay systems on small-world networks. We found that for adequate coupling strength and time delay, the whole dynamical networks can lead to better synchronization than the undelayed case. Thirdly, Based on multiple delay feedback control, some linear feedback controllers are constructed.The effect of the proposed control scheme on BA network is demonstrated via simulations, using as the units the Chua's system, Baier-Sahle system and Ikeda model. Finally, According to the presence of degree ordering among nodes of BA network, we choose the weights over the network connections. Numerical results show that the asymmetry of interactions has a great effect on the consensus. In the case that the interaction is dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/229362
Collection物理科学与技术学院
Recommended Citation
GB/T 7714
祁伟. 时滞系统与复杂动力学网络的研究[D]. 兰州. 兰州大学,2009.
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