Projective synchronisation with non-delayed and delayed coupling in complex networks consisting of identical nodes and different nodes

This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes. Based on Lyapunov stability theory, several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks; simultaneously the topological structure of the drive dynamical complex networks can be exactly identified. Moreover, numerical examples are presented to verify the feasibility and effectiveness of the theorems.

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some 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.

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.

Exponential Synchronization of Uncertain Complex Dynamical Networks with Delay Coupling

This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.

Adaptive synchronization in an array of asymmetric coupled neural networks

This paper investigates the global synchronization in an array of linearly coupled neural networks with constant and delayed coupling. By a simple combination of adaptive control and linear feedback with the updated laws, some sufficient conditions are derived for global synchronization of the coupled neural networks. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the realistic network. It is shown that the approaches developed here extend and improve the earlier works. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

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.

Noise analysis and measurement of time delay and integration charge coupled device

Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.

Distributed Synchronization of Coupled Time-Delay Neural Networks Based on Randomly Occurring Control

In this paper, the distributed synchronization of stochastic coupled neural networks with time-varying delay is concerned via randomly occurring control. We use two Bernoulli stochastic variables to describe the occurrence of distributed adaptive control and updating law according to certain probabilities. The distributed adaptive control and updating law for each vertex in the network depend on the state information on each vertex’s neighborhood. Based on Lyapunov stability theory, Itô differential equations, etc., by constructing the appropriate Lyapunov functional, we study and obtain sufficient conditions for the distributed synchronization of such networks in mean square.

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Design and implementation of high speed TDI CCD timing-driven circuits

The time delay integration charge coupled device(TDI CCD)is the key component in remote sensing systems.The paper analyzes the structure and the working principles of the device according to a customized TDI CCD chip.Employing the special clock resources and large-scale phase locked logic(PLL)in field-programmable gate arrays(FPGA),a timing-driven approach is proposed,using which all timing signals including reset gate,horizontal and vertical timing signals,are implemented in one chip.This not only reduces printed circuit board(PCB)space,but also enhances the portability of the system.By studying and calculating CCD parameters thoroughly,load capacity and power consumption,package,etc,are compared between various candidates chips,and detailed comparison results are also listed in table.Experimental results show that clock generator and driving circuit satisfy the requirements of high speed TDI CCD.

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.

Topology inference of uncertain complex dynamical networks and its applications in hidden nodes detection

The topological structure of a complex dynamical network plays a vital role in determining the network＇s evolutionary mecha- nisms and functional behaviors, thus recognizing and inferring the network structure is of both theoretical and practical signif- icance. Although various approaches have been proposed to estimate network topologies, many are not well established to the noisy nature of network dynamics and ubiquity of transmission delay among network individuals. This paper focuses on to- pology inference of uncertain complex dynamical networks. An auxiliary network is constructed and an adaptive scheme is proposed to track topological parameters. It is noteworthy that the considered network model is supposed to contain practical stochastic perturbations, and noisy observations are taken as control inputs of the constructed auxiliary network. In particular, the control technique can be further employed to locate hidden sources （or latent variables） in networks. Numerical examples are provided to illustrate the effectiveness of the proposed scheme. In addition, the impact of coupling strength and coupling delay on identification performance is assessed. The proposed scheme provides engineers with a convenient approach to infer topologies of general complex dynamical networks and locate hidden sources, and the detailed performance evaluation can further facilitate practical circuit design.

Synchronization-Based Topology Identification of Uncertain Stochastic Delay Complex Networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.