Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N＋1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

In this paper, the pinning synchronization between two fractional complex dynamical networks with nonlinear coupling, time delays and external disturbances is investigated. A Lyapunov-like theorem for the fractional system with time delays is obtained. A class of novel controllers is designed for the pinning synchronization of fractional complex networks with disturbances. By using this technique, fractional calculus theory and linear matrix inequalities, all nodes of the fractional complex networks reach complete synchronization. In the above framework, the coupling-configuration matrix and the innercoupling matrix are not necessarily symmetric. All involved numerical simulations verify the effectiveness of the proposed scheme. © 2017 Chinese Association of Automation.

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.

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed： （1） what nodes should be selected as pinned candidates？ （2） How many nodes are needed to be pinned for a fixed coupling strength？ Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.

Steimann Pin Repair of Zygomatic Complex Fractures

Purpose: To present the treatment of zygomaticomaxillary complex (ZMC) fractures with closed-reduction Steinmann-pin fixation and to compare it to the reduction and aesthetic outcomes of open-reduction techniques (ORIF). Materials and Methods: Case series. Charts for 23 patients with ZMC fractures presenting to the Head and Neck Surgery Department at Harbor-UCLA Medical Center from 2005 to 2009 were reviewed. Pre- and post-operative computed tomography (CT) scans were analyzed. Follow up ranged from 3 to 55 months. Interviews were conducted to evaluate the patient’s satisfaction. Patients were placed in two groups: those treated with ORIF and those treated with closed-reduction Steinmann-pin fixation. Results: Twelve patients had complete data for analysis. Average operative time was significantly lower for patients treated with closed-reduction as compared to open-reduction: 65.3 minutes vs. 162.5 minutes (p = 0.02). Bony realignment and aesthetic results were comparable in both groups. Additionally, only one 1cm facial incision was required with this repair system versus several incisions using traditional methods. Conclusions: Closed-reduction Steinmann-pin fixation of ZMC fractures provides adequate bony alignment and aesthetics. Our study supports this system in the repair of ZMC fractures as it requires significantly less operating time, one small incision, and excellent patient outcomes.

Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes.We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths.Based on the Lyapunov-Krasovskii stability theory for functional differential equations and a linear matrix inequality（LMI）,some sufficient conditions for the synchronization are derived.A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.

Pinning control of complex Lur’e networks

This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

Comparison between pinning control of different chaotic complex dynamical networks

The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.

基于销/盘试验机的摩擦噪声试验与仿真研究

为了研究摩擦噪声的产生机制和影响因素,利用销/盘试验机对以转子式压缩机曲轴-法兰材料制成的销/盘试样进行摩擦噪声试验研究;应用ABAQUS有限元软件,建立销/盘试验机有限元模型,利用复特征值分析方法预测该系统摩擦噪声的主频,并与试验结果进行对比;讨论相关参数对系统的稳定性和摩擦噪声的影响。结果表明:销与盘法向和横向振动的耦合是引起系统自激振动和摩擦噪声的重要因素;当系统摩擦界面处的摩擦因数大于系统临界摩擦因数时,系统开始出现不稳定振动,且摩擦因数越大,系统越不稳定,越易出现摩擦噪声;法向载荷对系统稳定性的影响不大;选择具有合适弹性模量的摩擦副材料可以抑制摩擦噪声的产生。

Controlled synchronization of complex network with different kinds of nodes

In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are performed for verification and illustration.

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper, the pinning synchronization problem of stochastic delayed complex network （SDCN） is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller, where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller, some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.

Coordinated chaos control of urban expressway based on synchronization of complex networks

We investigate the problem of coordinated chaos control on an urban expressway based on pinning synchronization of complex networks. A node coupling model of an urban expressway based on complex networks has been established using the cell transmission model（CTM）. The pinning controller corresponding to multi-ramp coordinated controller was designed by using the delayed feedback control（DFC） method, whose objective is to realize periodical orbits from chaotic states. The concrete pinning control nodes corresponding to the subsystems of regulating the inflows from the on-ramps to the mainline were obtained and the parameters of the controller were optimized by using the stability theory of complex networks to ensure the network synchronization. The validity of the proposed coordinated chaos control method was proven via the simulation experiment. The results of the examples indicated that the order motion on urban expressway can be realized, the wide-moving traffic jam can be suppressed, and the operating efficiency is superior to that of the traditional control methods.

Complex tree: the basic framework of protein-protein interaction networks

In living cells, proteins are dynamically connec ted through biochemical reactions, so its functi onal features are properly encoded into protein protein interaction networks (PINs). Up to pres ent, many efforts have been devoted to exploring the basic feature of PINs. However, it is still a challenging problem to explore a universal pr operty of PINs. Here we employed the complex networks theory to analyze the proteinprotein interactions from Database of Interacting Prot ein. Complex tree: the unique framework of PINs was revealed by three topological properties of the giant component of PINs (GCOP), including rightskewed degree distributions, relatively sm all clustering coefficients and short characteristic path lengths. Furthermore, we proposed a no nlinearly growth model: complex tree model to reflect the tree framework, the simulation resu lts of this model showed that GCOPs were well represented by our model, which could be help ful for understanding the treestructure: basic framework of PINs. Source code and binaries freely available for download at http://cic.scu. edu.cn/bioinformatics/STM/STM_code.rar.

Generalized projective synchronization of fractional-order complex networks with nonidentical nodes

This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.

On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

This paper investigates the synchronization of directed networks whose coupling matrices are reducible and asymmetrical by pinning-controlled schemes. A strong sufficient condition is obtained to guarantee that the synchronization of the kind of networks can be achieved. For the weakly connected network, a method is presented in detail to solve two challenging fundamental problems arising in pinning control of complex networks: (1) How many nodes should be pinned? (2) How large should the coupling strength be used in a fixed complex network to realize synchronization? Then, we show the answer to the question that why all the diagonal block matrices of Perron-Frobenius normal matrices should be pinned? Besides, we find out the relation between the Perron-Frobenius normal form of coupling matrix and the differences of two synchronization conditions for strongly connected networks and weakly connected ones with linear coupling configuration. Moreover, we propose adaptive feedback algorithms to make the coupling strength as small as possible. Finally, numerical simulations are given to verify our theoretical analysis.

周期间歇性牵制控制的复杂网络有限时间同步

针对具有时变时滞的复杂网络有限时间同步问题,提出了基于周期间歇性牵制控制的同步方法。通过构造Lyapunov-Krasovskii泛函,并基于有限时间稳定性理论、矩阵理论和不等式技巧,给出了有向网络和无向网络分别实现有限时间同步的充分条件,并讨论了有向网络和无向网络在实现有限时间同步时所需牵制的关键节点的最少数量以及如何选择关键节点。同时,结合周期间歇性控制策略和牵制控制策略,设计出了有限时间周期间歇性牵制控制器,最后利用数值模拟验证了结果的正确性和有效性。

基于复杂网络视角的供应链脆弱性预防和应对策略

分析了供应链网络的复杂网络相关特性,揭示了供应链网络脆弱性的产生机理;基于复杂网络的视角,研究了供应链网络脆弱性的预防策略;并运用牵制控制和弱连接理论研究了供应链网络发生中断或者发生突发事件后的应对策略。

牵制控制下复杂网络的同步性研究

复杂网络是由数量巨大的节点组成,任何人都无法控制所有节点.只有通过控制少数节点,对复杂网络进行牵制控制,才能达到网络同步的目的.为此分析了一般网络和含有生成树的网络同步的条件,给出了实现算法及运行界面.仿真结果表明,随着网络规模的扩大,驱动节点的比例减小,驱动节点常常都是入度低的节点.