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非线性网络的动力学复杂性研究 总被引:1,自引:0,他引:1
综述了非线性网络的动力学复杂性研究在网络理论、实证和应用方面所取得的主要进展和重要成果;深刻揭示了复杂网络的若干复杂性特征与基本定量规律;提出和建立了网络科学的统一混合理论体系(三部曲)和网络金字塔,并引入一类广义Farey组织的网络家族,阐明网络的复杂性-简单性与多样性-普适性之间转变关系;揭示了网络的拓扑结构特征与网络的动态特性之间关系;建立具有长程连接的规则网络的部分同步理论并应用于随机耦合的时空非线性系统的同步;提出复杂网络的动力学同步与控制多种方法;提出若干提高同步能力的模型、方法和途径,如同步最优和同步优先模型、同步与网络特征量关系、权重作用、叶子节点影响等;提出复杂混沌网络的多目标控制及具有小世界和无标度拓扑的束流输运网络的束晕一混沌控制方法;提出集群系统的自适应同步模型及蜂拥控制方法;探讨网络上拥塞与路由控制、资源博弈及不同类型网络上传播的若干规律;揭示含权经济科学家合作网及其演化特点;实证研究并揭示了多层次的高科技企业网和若干社会网络的特点;提出一种复杂网络的非平衡统计方法,把宏观网络推进到微观量子网络. 相似文献
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综述了非线性网络的动力学复杂性研究在网络理论、实证和应用方面所取得的主要进展和重要成果;深刻揭示了复杂网络的若干复杂性特征与基本定量规律;提出和建立了网络科学的统一混合理论体系(三部曲)和网络金字塔,并引入一类广义Farey组织的网络家族,阐明网络的复杂性-简单性与多样性-普适性之间转变关系;揭示了网络的拓扑结构特征与网络的动态特性之间关系;建立具有长程连接的规则网络的部分同步理论并应用于随机耦合的时空非线性系统的同步;提出复杂网络的动力学同步与控制多种方法;提出若干提高同步能力的模型、方法和途径,如同步最优和同步优先模型、同步与网络特征量关系、权重作用、叶子节点影响等;提出复杂混沌网络的多目标控制及具有小世界和无标度拓扑的束流输运网络的束晕-混沌控制方法;提出集群系统的自适应同步模型及蜂拥控制方法;探讨网络上拥塞与路由控制、资源博弈及不同类型网络上传播的若干规律;揭示含权经济科学家合作网及其演化特点;实证研究并揭示了多层次的高科技企业网和若干社会网络的特点;提出一种复杂网络的非平衡统计方法,把宏观网络推进到微观量子网络。 相似文献
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为了提高环状网络保密通信的安全性,分析时滞干扰对环状网络同步的影响。首先根据环状网络的拓扑结构,构造时变时滞干扰环状网络的数学模型,然后基于Lyapunov稳定性方法,设计自适应控制器控制环状网络,实现无时滞、常时滞和时变时滞干扰环状网络的修正函数投影同步,说明该自适应控制器具有普适性。通过数值仿真验证了理论分析的正确性,同时发现时滞干扰会降低环状网络的同步能力,时滞值越大,同步能力越差,实现同步所需的时间越长。 相似文献
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针对具有时变时滞耦合的两个不同复杂网络, 研究其广义同步问题. 基于Barbalat引理, 设计非线性自适应控制器使得两个网络获得广义同步. 进一步研究了具有未知拓扑结构的两个网络的广义同步问题. 数值仿真表明了本文方法的有效性. 相似文献
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加权网络可以对复杂系统的相互作用结构提供更加细致的刻画,而改变边权也成为调整和改善网络性质与功能的新途径.基于已有无权网络的效率概念,文中给出了相似权和相异权网络的网络效率定义,并研究了权重分布对于网络效率的影响.从平权的规则网络出发,通过改变权重的分布形式考察权重分布对网络效率的影响,结果发现,在规则网络上,权重分布随机性的增加提高了网络效率,而在几种常见的权重分布形式中,指数分布对网络效率的改进最为显著.同时,权重随机化之后网络最小生成树的总权重减小,意味着网络的运输成本随着权重异质性的增加而降低.以上结果为深入理解权重对网络结构与功能的影响提供了基础.
关键词:
复杂网络
加权网络
权重
网络效率 相似文献
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《Physics letters. A》2014,378(5-6):514-518
We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification. 相似文献
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This paper regards the outer synchronization between two delay-coupled complex dynamical networks with nonidentical topological structures and a noise perturbation. Considering one network as the drive network and the other one as the response network, the drive-response system achieves synchronous states through a suitably designed adaptive controller. The stochastic LaSalle invariance principle is employed to theoretically prove the almost sure synchronization between two networks. Finally, two numerical examples are examined in order to illustrate the proposed synchronization scheme. 相似文献
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Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions 下载免费PDF全文
<正>The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper.Based on Lyapunov stability theory and Barbalat’s lemma,generalized matrix projective lag synchronization criteria are derived by using the adaptive control method.Furthermore,each network can be undirected or directed,connected or disconnected,and nodes in either network may have identical or different dynamics.The proposed strategy is applicable to almost all kinds of complex networks.In addition,numerical simulation results are presented to illustrate the effectiveness of this method,showing that the synchronization speed is sensitively influenced by the adaptive law strength,the network size,and the network topological structure. 相似文献
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Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application 下载免费PDF全文
Yong-Bing Hu 《中国物理 B》2022,31(11):110501-110501
Multi-link networks are universal in the real world such as relationship networks, transportation networks, and communication networks. It is significant to investigate the synchronization of the network with multi-link. In this paper, considering the complex network with uncertain parameters, new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization (FTCPS). In addition, based on fractional-order Lyapunov functional method and finite-time stability theory, the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters. Meanwhile, numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters. Finally, the network is applied to image encryption, and the security analysis is carried out to verify the correctness of this method. 相似文献
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We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach. 相似文献
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We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach. 相似文献
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Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network 下载免费PDF全文
<正>This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays.Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations,as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks.It is shown that,through Lyapunov stability theory,distributed adaptive controllers constructed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks,and perturbation inputs.A Chua's circuit network example is finally given to show the effectiveness of the proposed synchronization criteria. 相似文献
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利用非对称非线性函数耦合混沌同步方法,讨论了Chen吸引子的混沌同步问题,数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响. 将非对称非线性函数耦合同步方法进一步推广发展到完全连接网络和由星形子网络构成的复杂大网络混沌同步的研究中. 提供了确定网络中神经元之间混沌同步状态稳定性的误差发展方程,并讨论各个耦合强度因子对网络同步稳定性过程的影响,给出了相应的稳定性范围. 通过数值模拟证明利用非线性函数作为耦合函数,实现完全连接网络、星形子网络构成大网络的混沌同步是有效的. 可以预测在网络的混沌同步
关键词:
非线性耦合函数
Chen吸引子
混沌同步
网络 相似文献