非线性耦合的复杂网络自适应同步

提出了一种通过非线性耦合的复杂网络自适应同步方案,方案具有自适应律简单和应用范围广等特点。证明了动力系统满足给定条件下,该同步方案同步,且同步解是局部和全局渐进稳定的。两个计算机仿真实例分别展示了在无标度网络和最近邻耦合网络上的同步误差变化趋势,验证了同步方案的有效性。     

Synchronization of Uncertain Complex Networks with Time‐Varying Node Delay and Multiple Time‐Varying Coupling Delays

This paper investigates the synchronization problem of a class of complex dynamical networks via an adaptive control method. It differs from existing works in considering intrinsic delay and multiple different time‐varying coupling delays, and uncertain couplings. A simple approach is used to linearize the uncertainties with the norm‐bounded condition. Simple but suitable adaptive controllers are designed to drive all nodes of the complex network locally and globally synchronize to a desired state. In addition, several synchronization protocols are deduced in detail by virtue of Lyapunov stability theory and a Cauchy matrix inequality. Finally, a simulation example is presented, in which the dynamics of each node are time‐varying delayed Chua chaotic systems, to demonstrate the effectiveness of the proposed adaptive method.     

基于自适应事件触发牵制控制的多时滞随机耦合神经网络簇同步

本文通过自适应事件触发牵制控制策略,研究了多时滞的随机耦合神经网络在均方意义下以指数速率进行簇同步的问题.在耦合神经网络中,同一簇中的节点只需与相应的孤立节点同步,而对于不同簇中节点之间的同步状态没有要求.首先,本文提出了一种事件触发牵制控制方法来解决耦合神经网络中节点数量众多、通讯复杂的问题.该方法不仅能减少耦合神经网络中控制器的数量,还可以减少控制信号的传输次数、减轻网络传输压力.然后根据M矩阵方法,建立了随机耦合神经网络均方指数稳定的充分条件.同时,利用自适应控制策略,给出了反馈增益的更新规律.最后,通过一个数值例子验证了所提出的自适应事件触发牵制控制策略的有效性和适用性.     

Pinning‐controlled synchronization of hybrid‐coupled complex dynamical networks with mixed time‐delays

This paper investigates the pinning‐controlled synchronization of a general complex dynamical network with hybrid coupling, which includes constant coupling, discrete‐delay coupling and distributed‐delay coupling. Furthermore, the network can be composed of coupled identical nonlinear oscillators with or without internal time‐delay. To be more consistent with the realistic networks, the internal time‐delay, the discrete time‐delay and the distributed time‐delay can be different from each other, the inner coupling matrices are not necessarily to be diagonal, and the coupling configuration matrices are not required to be symmetric or irreducible. Under some sufficient conditions, it is shown that a hybrid‐coupled complex network with or without internal time‐delay can be asymptotically pinned to a homogenous trajectory by applying adaptive control actions to a small fraction of network nodes. In particular, the paper addresses what kind of nodes should be pinned and how many nodes are needed to be pinned to achieve synchronization in a hybrid‐coupled network with fixed coupling matrices and strengths. Numerical examples are given to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

时变耦合复杂网络同步的自适应控制

应用自适应控制策略实现时变耦合复杂网络的同步。通过构造layapunov函数,证明了对于任意初始状态的时变耦合复杂动力学网络模型在相应的控制手段下总可以实现渐近同步,数值仿真证实了此控制策略的有效性。     

Synchronization of Complex Networks with Coupled and Self‐Feedback Delays Via Aperiodically Intermittent Strategy

In this paper, we concern the exponential synchronization problem for hybrid‐coupled delayed dynamical networks via aperiodically intermittent control. Different from previous works, the delayed coupling term considered here contains the transmission delay and self‐feedback delay, and the intermittent control can be aperiodic. By utilizing a different technique compared with some previous results, several useful criteria are derived analytically to realise exponential synchronization for a class of coupled complex network. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural network are obtained. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

On pinning synchronization of complex dynamical networks

There exist some fundamental and yet challenging problems in pinning control of complex networks: (1) What types of pinning schemes may be chosen for a given complex network to realize synchronization? (2) What kinds of controllers may be designed to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? This paper addresses these technique questions. Surprisingly, it is found that a network under a typical framework can realize synchronization subject to any linear feedback pinning scheme by using adaptive tuning of the coupling strength. In addition, it is found that the nodes with low degrees should be pinned first when the coupling strength is small, which is contrary to the common view that the most-highly-connected nodes should be pinned first. Furthermore, it is interesting to find that the derived pinning condition with controllers given in a high-dimensional setting can be reduced to a low-dimensional condition without the pinning controllers involved. Finally, simulation examples of scale-free networks are given to verify the theoretical results.     

考虑树突整合效应的神经元网络的放电和同步特性

生物神经网络的同步被认为在大脑神经信息的处理过程中发挥了重要作用.本文在Hodgkin-Huxley(HH)神经元网络模型中考虑树突整合效应,得到修正后的DHH(Dendritic-integration-rule-based HH)神经元网络模型,研究了网络的放电和同步特性.首先以三个抑制性神经元构成的耦合系统为例,发现树突整合效应的加入提高了神经元的放电阈值;然后分别建立全局耦合的抑制性和兴奋性神经元网络,发现大的耦合强度能够诱导抑制性和兴奋性神经元网络达到几乎完全同步的状态,并且对神经元的放电幅值有较大的影响;更有趣的是,当树突整合系数为某一值时,抑制性神经元网络的同步达到最高,而兴奋性神经网络的同步达到最低.     

Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller

This paper investigates the generalized projective synchronization (GPS) among the nodes within a complex dynamical network (CDN). Multiple characteristics of realistic networks are simultaneously considered in our network model. First, one crucial node is introduced into our CDN, which behaves like a leader and exists in many practical networks. Second, the commonalities between the crucial node and every other node are discussed and they are embodied in the network model. Third, our CDN is composed of different dimensional nodes and has an overall time‐varying coupling strength. Furthermore, in order to describe more synchronous phenomena, the exponential generalized projective synchronization (EGPS) and asymptotic generalized projective synchronization (AGPS) are defined. The main objective of this paper is to design an effective but simple decentralized controller for the crucial node such that our network realizes GPS. Based on rigorous theoretical derivations, EGPS and AGPS schemes are respectively proposed according to whether the overall coupling strength is certain or adaptive. Few previous studies have focused on this. It is worth pointing out that both the control input and the adaptive law of the coupling strength in this paper only lie in the information of the crucial node, which implies the significance of the crucial node to some extent. Finally, the effectiveness and feasibility of our theoretical results are verified by two numerical simulation examples.     

复杂动力学网络的自适应线性广义同步及参数识别

针对参数未知的复杂动力学网络，基于Lyapunov稳定性理论和LaSMle不变原理，通过设计合适的自适应控制器不仅实现了参数未知的复杂动力学网络之间的线性广义同步，而且对网络中的未知参数进行了追踪识别．文中设计的控制器对一类复杂动力学网络有普适性，并且由于其具有的自适应功能，使得该控制方法有鲁棒性．数值仿真结果进一步验证了控制方法的有效性与可行性．     

Pinning control of a generalized complex dynamical network model

This paper investigates the local and global synchronization of a generalized complex dynamical network model with constant and delayed coupling. Without assuming symmetry of the couplings, we proved that a single controller can pin the generalized complex network to a homogenous solution. Some previous synchronization results are generalized. In this paper, we first discuss how to pin an array of delayed neural networks to the synchronous solution by adding only one controller. Next, by using the Lyapunov functional method, some sufficient conditions are derived for the local and global synchronization of the coupled systems. The obtained results are expressed in terms of LMIs, which can be efficiently checked by the Matlab LMI toolbox. Finally, an example is given to illustrate the theoretical results.     

具有脉冲耦合复杂时滞动力网络的同步

考虑了一个具有脉冲耦合的复杂时滞动力网络的同步问题.基于脉冲时滞动力系统扩展的Halanay不等式,给出了网络同步的一个充分条件.所获结果表明,即使网络节点之间仅在一些离散时刻存在瞬时连接,网络仍然能够达到同步.进一步将所得结果应用于一个由混沌FHN神经元振子为动力节点所构成的一个无标度的动力网络,数值仿真结果表明了理...     

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

This paper is concerned with the problem of synchronization of complex dynamical networks with state and coupling time‐delays. Therefore, larger class and more complicated complex dynamical networks could be considered for the synchronization problem. Based on the Lyapunov‐Krasovskii functional, some delay‐independent and delay‐dependent criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the synchronization between each node of the complex dynamical network. The effectiveness of the proposed method is illustrated using some numerical simulations.     

带有未知参数的驱动-响应网络的自适应同步

研究由带有未知参数的混沌系统作为节点动力学构成的驱动-响应网络的自适应同步.基于Lyapunov稳定性理论以及LaSalle不变原理,设计合适的控制器和参数更新规则,使得驱动系统与响应网络达到同步.为了验证理论的正确性,选择加权网络和BA无标度网络作为数值例子,并比较相同网络结构下不同的节点动力学对同步时间的影响.数值...     

一种节能的无线传感器网络多跳自适应时间同步算法

研究能量长期有效的时间同步协议是成功部署生命力强的无线传感器网络的一项关键策略,对此,提出一种低能耗的多跳自适应时间同步算法（MATS：Multi-hop adaptive time synchronization）,该算法设计了一套灵活的机制来调整同步模式、全网重同步周期以及每对节点同步时的信标数,并且利用最大似然估计原理同时对节点的时钟偏移和频率偏移进行估计,达到用最小的能量损耗完成长期的、全网的时间同步的目的,最后通过数学分析和仿真的方法对所提出的改进算法进行了验证。     

Consecutive Synchronization of a Delayed Complex Dynamical Network via Distributed Adaptive Control Approach

In this paper, a consecutive synchronization scheme is investigated to synchronize the nodes of a delayed complex dynamical network with an isolated node via an adaptive control approach. The specific feature of this scheme consists in the structure of the communication links: a communication connection is required between the isolated node and one selected node in the network, and further communication links exist between any node and one neighbor node. In this way, all nodes are connected together like a chain. Based on Lyapunov-Krasovskii theory, some conditions are obtained in the form of linear matrix inequalities to guarantee the consecutive synchronization by the designed distributed adaptive control. To make this synchronization scheme more practical, no constraints have been considered for coupling connection matrix such as being symmetric or zero row sum. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.     

时变内耦合复杂网络的平衡态同步smart变结构控制

当前同步控制问题是复杂网络研究的热点之一. 本文针对具有时变内耦合结构的复杂网络, 利用结点混沌动态的各态历经性, 通过构造合适的滑模面, 提出了smart变结构控制器的设计策略. 该策略可使复杂网络动态行为趋向于所构造的全局吸引区域, 从而最终实现复杂网络在平衡态的渐近同步. 最后, 基于3种不同拓扑结构的Lorenz结点动态的复杂网络进行仿真实验表明该控制方案具有较好的鲁棒性和有效性.     

EEG信号构建的复杂网络同步稳定性分析

人脑是自然界最复杂的系统之一,脑网络作为复杂网络理论在神经科学中的重要应用,为脑疾病的病理机制提供了新的研究方向。同步性作为影响网络性能的指标,对于复杂网络有着重要影响。为了研究同步性在脑网络中的表现,利用EEG动力学方程对120例酗酒病人的EEG信号进行复杂网络模型构造,根据所构造的模型利用李雅普诺夫稳定性理论进行证明。并通过实验对正常人和酗酒者脑网络同步状态做出统计,给出了酗酒病人和正常人的脑网络同步差异,可以揭示酗酒疾病对于人脑在功能结构上的影响,对其他疾病提供研究思路。     

Synchronization of uncertain complex dynamical networks via adaptive control

In this paper, synchronization of an uncertain dynamical network with time‐varying delay is investigated by means of adaptive control schemes. Time delays and uncertainties exist universally in real‐world complex networks. Especially, parameters of nodes in these complex networks are usually partially or completely uncertain. Considering the networks with unknown or partially known nodes, we design adaptive controllers for the corresponding complex dynamical networks, respectively. Several criteria guaranteeing synchronization of such systems are established by employing the Lyapunov stability theorem. Analytical and numerical results show that the proposed controllers have high robustness against parameter variations including network topologies, coupling structures, and strength. Copyright © 2008 John Wiley & Sons, Ltd.     

精分EEG脑网络同步稳定性研究

为了深入表征和刻画精神分裂症患者大脑活动时各个电极通道的状态变化，通过利用复杂网络同步稳定理论以及精分工作记忆实验范式对EEG信号进行分析。从复杂网络角度出发构建脑功能网络，并利用特征谱比值法分析脑网络及其同步性随时间的演化过程。对比实验表明精分患者和正常对照组同步能力具有很大差异且差异主要源于对应脑网络的一个局部化区域S的不同，并通过设计对比实验进一步验证此区域对脑网络同步影响的有效性。脑网络同步稳定区域S的发现对研究神经精神性疾病下脑网络的演化过程提供了新的思路。