Synchronization in complex dynamical networks with nonsymmetric coupling

Based on the work of Nishikawa and Motter, who have extended the well-known master stability framework to include non-diagonalizable cases, we develop another extension of the master stability framework to obtain criteria for global synchronization. Several criteria for global synchronization are provided which generalize some previous results. The Jordan canonical transformation method is used in stead of the matrix diagonalization method. Especially, we show clearly that, the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second-largest eigenvalue, even though all the eigenvalues of the nonsymmetric coupling matrix are real. Furthermore, the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed. Numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two-cell cellular neural network.     

Synchronization of complex community networks with nonidentical nodes and adaptive coupling strength

In this Letter, the complex dynamical networks with community structure and nonidentical nodes are considered. The globally asymptotical synchronization of the time-delayed complex community networks onto any uniformly smooth state is studied. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strength. Finally, the developed techniques are applied to two complex community networks which are respectively synchronized to a chaotic trajectory and a periodic orbit, and numerical simulations are provided to show the feasibility of the developed methods.     

Synchronization analysis of delayed complex networks via adaptive time-varying coupling strengths

In this Letter, we study the synchronization for delayed complex networks by adjusting time-varying coupling strengths. Under some assumptions, the update laws of the coupling strengths are obtained to realize the synchronization based on Lassalle-Yoshizawa theorem. For the given delayed complex network, we can always find appropriate coupling strengths to achieve the synchronization. Compared with the existing results, the update laws don't need the information of the characteristics of the identical node and the coupling matrix. The state-dependencies of coupling strengths coupled to the dynamics of the nodes in a way to enhance synchronization. An example shows the proposed theoretical result is feasible and effective.     

Synchronization criteria for complex dynamical networks with neutral-type coupling delay

A generalized complex dynamical networks model with neutral-type coupling delay is proposed, which is an extension for the systems without time delay and with the retarded delay. By some transformation, the synchronization problem of the complex networks is transferred equally into the asymptotical stability problem of a group of uncorrelated neutral delay functional differential equations. Furthermore, the less conservative sufficient conditions for both delay-independent and delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities based on the free weighting matrix strategy. Numerical examples are given to illustrate the theoretical results.     

Pinning sampled-data synchronization for complex networks with probabilistic coupling delay

We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.     

Synchronization in complex delayed dynamical networks with impulsive effects

The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations.     

Synchronization for complex dynamical Lurie networks

This paper investigates the synchronization problem for two different complex dynamical Lurie networks, The first one is with constant coupling and the second one is with constant coupling and discrete-delay coupling. Based on contraction theory and matrix measure properties, some new delay-independent synchronization conditions depending on coupling strength and network topology are proposed. Finally, simulation results are presented to support the theoretical results.     

Synchronization in Oscillator Networks with Nonlinear Coupling

Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also eventually dissipative under the hypothesis of eventual dissipation of the uncoupled oscillators. And the dynamics of the network is analyzed in its absorbing domain by combining two methods developed recently. Suufficient conditions for synchronization in the oscillator networks with nonlinear coupling are obtained. The two methods are combined effectively and the results embody the respective merits of the two methods. Numerical simulations confirm the validity of the results.     

Erratum to: “Controlling complex dynamical networks with coupling delays to a desired orbit” [Phys. Lett. A 359 (2006) 42]

In this Letter, we indicate that the proposed sufficient condition in Letter [Z. Li, G. Feng, D., Hill, Phys. Lett. A 359 (2006) 42] does not hold, which cannot guarantee that the states of complex network with coupling delays globally exponentially synchronize with a desired orbit and it only applies to globally asymptotical synchronization with a desired orbit. For correcting the mistakes, a correct version of globally exponential synchronization is given and proved in this Letter.     

Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay

This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm~g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.     

Synchronization in an array of linearly stochastically coupled networks with time delays

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.     

Synchronization in a class of weighted complex networks with coupling delays

It is commonly accepted that realistic networks can display not only a complex topological structure, but also a heterogeneous distribution of connection weights. In addition, time delay is inevitable because the information spreading through a complex network is characterized by the finite speeds of signal transmission over a distance. Weighted complex networks with coupling delays have been gaining increasing attention in various fields of science and engineering. Some of the topics of most concern in the field of weighted complex networks are finding how the synchronizability depends on various parameters of the network including the coupling strength, weight distribution and delay. On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state. Finally, an example is given as an illustration testing the theoretical results.     

Global synchronization for a class of dynamical complex networks

This paper is concerned with the problem of global synchronization for a class of dynamical complex networks composed of general Lur’e systems. Based on the absolute stability theory and the Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions are established to guarantee global synchronization of dynamical networks with complex topology, directed and weighted couplings. Several global synchronization criteria formulated in the form of linear matrix inequalities (LMIs) or frequency-domain inequalities are also proposed for undirected dynamical networks. In order to obtain global results, no linearization technique is involved through derivation of the synchronization criteria. Numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Synchronization analysis of delayed complex networks with time-varying couplings

In this paper, a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays. The coupling configurations are not restricted to the symmetric and irreducible connections or the non-negative off-diagonal links. The stability criteria are obtained by using Lyapunov-Krasovskii functional method and subspace projection method. These criteria reveal the relationship between coupling matrices and stability of the dynamical networks.     

Periodic synchronization of community networks with non-identical nodes uncertain parameters and adaptive coupling strength

In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle＇s invariance principle, a cri- teflon is established by constructing an effective control identification scheme and adjusting automatically the adaptive coupling strength. The proposed control law is applied to a complex community network which is periodically synchro- nized with different chaotic states. Numerical simulations are conducted to demonstrate the feasibility of the proposed method.     

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

<正>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.     

Coupling transfer matrix method to finite element method for analyzing the acoustics of complex hollow body networks

This paper exposes a procedure to couple multiport transfer matrices to finite elements for analyzing the acoustics of automotive hollow body networks with a minimum of memory requirements and computational time. Generally, hollow body networks are made up from a series of elongated fluid partitions similar to ducts or waveguides. These fluid partitions generally contain complex elements: junctions, noise control elements, and cavities. The location and type of these elements in the network, mainly the noise control elements (e.g., sealing parts), may impact the noise inside a car. In the proposed hybrid method, the elongated fluid partitions are modeled with fluid finite elements. All complexities are modeled with two-port or multiport transfer matrices. The coupling of these matrices to finite elements is naturally done at the weak integral formulation stage of the acoustical problem. The coupling does not add any degrees of freedom to, nor modify, the original finite element matrix system. Consequently, changing locations and types of noise control elements in the hollow body network is fast and does not require rebuilding the finite element system. This enables optimizing the acoustics of a complex network on a desktop computer. The hybrid method is compared to experimental results on a tee-shaped hollow body networks. Good correlations are obtained.     

Acoustic attenuation analysis of silencers with multi-chamber by using coupling method based on subdomain division technique

For multi-chamber silencers with non-uniform cross-sections at axial direction, the coupling method based on subdomain division technique is proposed. The silencer is divided into several subdomains which impedance matrixes are calculated by using suitable 3-D methods. Combining with the continuity conditions at the interfaces to solve the integral impedance matrix of the silencer, thereby the transmission loss is derived. For the double-chamber silencers, the transmission loss and computational speed results from the proposed method, the numerical mode matching (NMM) method, 3-D finite element (FE) method predictions and experimental measurements are compared, which verifies the accuracy and efficiency.     

Comment on “Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers” [Physica A 387 (2008) 2111-2119]

In this paper, we point out two problems in synchronization of dynamic networks based on linear feedback controllers presented by Wu and Jiao [J. Wu, L. Jiao, Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers, Physica A 387 (2008) 2111-2119]. Furthermore, an amendatory version on global exponential synchronization is given and proved in this paper.     

Transfer matrix methods for sound attenuation in resonators with perforated intruding inlets

A resonator with perforated intruding inlet (PII) is a superior silencer element, since the use of perforated inlet extensions can dramatically improve the acoustic performance. In this work, both a one-dimensional (1D) and a two-dimensional (2D) transfer matrix methods are developed to predict the transmission loss of the resonator without considering the mean flow. Based on the two groups of comparisons with tests, it is found out that the applicability of 1D method is limited by the resonator geometry even when the frequency is below the cut-off value of plane wave. Whereas the 2D approach is much more accurate while predicting the transmission losses within entire frequency range. Subsequently, five groups of resonators are chosen to determine the effects of structure parameters to transmission loss based on the 2D approach. The resonant frequency decreases and more resonant peaks appear when the length of inlet extension increases. A higher perforation rate leads to a shift of resonant peak towards higher frequencies. Besides, better acoustic performance could be obtained with the perforation being properly designed. Reducing the inlet/outlet radius can obviously improve the transmission loss without changing the frequency of resonant peak. The theories and conclusions in this study can be used for the design and optimization of resonators in various engineering applications.