Synchronization of stochastic complex networks with time-delayed coupling

Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.

Synchronization performance in time-delayed random networks induced by diversity in system parameter

Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network setting is appreciated to detect the stability and transition of collective behaviors in a network with different connection types. In this paper, the synchronization performance in time-delayed excitable homogeneous random networks（EHRNs） induced by diversity in system parameters is investigated by calculating the synchronization parameter and plotting the spatiotemporal evolution pattern, and distinct impacts induced by parameter-diversity are detected by setting different time delays. It is found that diversity has no distinct effect on the synchronization performance in EHRNs with small time delay being considered. When time delay is increased greatly, the synchronization performance of EHRN degenerates remarkably as diversity is increased. Surprisingly, by setting a moderate time delay, appropriate parameter-diversity can promote the synchronization performance in EHRNs, and can induce the synchronization transition from the asynchronous state to the weak synchronization. Moreover, the bistability phenomenon, which contains the states of asynchronous state and weak synchronization,is observed. Particularly, it is confirmed that the parameter-diversity promoted synchronization performance in time-delayed EHRN is manifested in the enhancement of the synchronization performance of individual oscillation and the increase of the number of synchronization transitions from the asynchronous state to the weak synchronization. Finally, we have revealed that this kind of parameter-diversity promoted synchronization performance is a robust phenomenon.

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.

Finite-time Mittag-Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.

A consensus time synchronization protocol in wireless sensor network

Time synchronization is one of the base techniques in wireless sensor networks(WSNs).This paper proposes a novel time synchronization protocol which is a robust consensusbased algorithm in the existence of transmission delay and packet loss.It compensates for transmission delay and packet loss firstly,and then,estimates clock skew and clock offset in two steps.Simulation and experiment results show that the proposed protocol can keep synchronization error below 2μs in the grid network of 10 nodes or the random network of 90 nodes.Moreover,the synchronization accuracy in the proposed protocol can keep constant when the WSN works up to a month.

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.

Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin–Huxley neurons

We numerically study the effect of the channel noise on the spiking synchronization of a scale-free Hodgkin-Huxley neuron network with time delays. It is found that the time delay can induce synchronization transitions at an intermediate and proper channel noise intensity, and the synchronization transitions become strongest when the channel noise intensity is optimal. The neurons can also exhibit synchronization transitions as the channel noise intensity is varied, and this phenomenon is enhanced at around the time delays that can induce the synchronization transitions. It is also found that the synchronization transitions induced by the channel noise are dependent on the coupling strength and the network average degree, and there is an optimal coupling strength or network average degree with which the synchronization transitions become strongest. These results show that by inducing synchronization transitions, the channel noise has a big regulation effect on the synchronization of the neuronal network. These findings could find potential implications for the information transmission in neural systems.

Adaptive Stochastic Synchronization of Uncertain Delayed Neural Networks

This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain parameters and stochastic perturbations, in which the controller is less conservative and optimal since its control gains can be automatically adjusted according to some designed update laws. Based on Lyapunov stability theory and Barbalat lemma, sufficient condition is obtained for synchronization of delayed neural networks by strict mathematical proof. Moreover, the obtained results of this paper are more general than most existing results of certainly neural networks with or without stochastic disturbances. Finally, numerical simulations are presented to substantiate our theoretical results.

Synchronization of Transient Delay-Coupled Network

A transient delay-coupled network was proposed by modifying the standard delay-coupled network with a transient coupling technique to enlarge the synchronization domain of the network, where the synchronization domain is the interval of the coupling strength for which the network gets synchronized. The coupling of the transient delay-coupled network is activated when the systems are in a particular region (coupling region) of the phase space and inactivated otherwise, which is different from the standard coupling. The specific synchronization performance of the transient delay-coupled network was investigated through case studies. The relationships between the synchronization domain and the coupling region were obtained by gauging the synchronization index. It is understood that the synchronization domain changes in a non-smooth manner with the variation of the coupling region. In particular, the synchronization domain of a transient delay-coupled network is much larger than that of the standard delay-coupled network when the coupling region is appropriately determined.

Dynamics of a multiplex neural network with delayed couplings

Multiplex networks have drawn much attention since they have been observed in many systems,e.g.,brain,transport,and social relationships.In this paper,the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied.The stability and bifurcation of the network equilibrium are discussed,and interesting neural activities of the network are explored.Based on the neuron circuit,transfer function circuit,and time delay circuit,a circuit platform of the network is constructed.It is shown that delayed couplings play crucial roles in the network dynamics,e.g.,the enhancement and suppression of the stability,the patterns of the synchronization between networks,and the generation of complicated attractors and multi-stability coexistence.

Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques

In this paper,the authors are concerned with global asymptotic synchronization for a class of BAM neural networks with time delays.Instead of using Lyapunov functional method,LMI method and matrix measure method which are recently widely applied to investigating global exponential/asymptotic synchronization for neural networks,two novel sufficient conditions on global asymptotic synchronization of above BAM neural networks are established by using a kind of new study method of global synchronization:Integrating inequality techniques.The method and results extend the study of global synchronization of neural networks.

Pinning Synchronization of Discrete-Time Complex Networks with Different Time-Varying Delays

This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchronization criteria for this kind of net works.The results provide an effective way to synchronize discrete-time complex networks by reducing control cost.Furthermore,these theoretical results are illustrated by a complex network via two kinds of pinning schemes.Numerical simulations verify the feasibil计y of the proposed methods.

Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed Ho~ and passive projective synchronization problem for fractional-order （FO） memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequaiity techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

Synchronization Research of a Modified Time-Delayed Multi-agent Network Model

The synchronization of time-delayed multi-agent networks with connected and directed topology is studied. Based on the correlative work about the agent synchronization, a modified model is presented, in which each communication receiver is distributed a delay 7. In addition, a proportional term k is introduced to modulate the delay range and to guarantee the synchronization of each agent. Two new parameters mentioned above are only correlative to the network topology, and a theorem about their connections is derived by both frequency domain method and geometric method. Finally, the theoretical result is illustrated by numerical simulations.

General Decay Synchronization for Recurrent Neural Networks with Mixed Time Delays

This paper studies the general decay synchronization(GDS)of a class of recurrent neural networks(RNNs)with general activation functions and mixed time delays.By constructing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques,some sufficient conditions on the GDS of considered RNNs are established via a type of nonlinear control.In addition,one example with numerical simulations is presented to illustrate the obtained theoretical results.

H∞ synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach

This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound.A delaydependent criterion for the H_∞synchronization is derived by employing the Lyapunov functional method together with some recent inequalities.Then,with the help of some decoupling techniques,sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases.Lastly,an example is used to illustrate the applicability of the results obtained.

Synchronization Transition of Time Delayed Complex Dynamical Networks with Discontinuous Coupling

This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.

Adaptive coupling-enhanced spiking synchronization in Newman-Watts neuronal networks with time delays

In this paper, we study how adaptive coupling with time-periodic growth speed (TPGS) affects the spiking synchronization of weighted adaptive Newman-Watts Hodgkin-Huxley neuron networks with time delays. It is found that the neuronal spiking intermittently exhibits synchronization transitions between desynchronization and in-phase synchronization or anti-phase synchronization as TPGS amplitude or frequency is varied, showing multiple synchronization transitions. These transitions depend on the values of time delay and can occur only when time delay is close to those values that can induce synchronization transitions when the growth speed is fixed. These results show that the adaptive coupling with TPGS has great influence on the spiking synchronization of the neuronal networks and thus plays a crucial role in the information processing and transmission in neural systems.

Mixed H_(∞)/Passive Exponential Synchronization for Delayed Memristive Neural Networks with Switching Event-Triggered Control

This paper is devoted to event-triggered synchronization of delayed memristive neural networks with H∞and passivity performance.The aim is to guarantee the exponential synchronization and mixed H∞and passivity control for memristive neural networks by using event-triggered control.Firstly,a switching system is constructed under the event-triggered control strategy.Then,by adopting a piece-wise Lyapunov functional,a sufficient condition is established for the exponential synchronization and mixed H_(∞)and passivity performance.Moreover,an event-triggered controller design scheme is proposed using matrix decoupling method.Finally,the effectiveness of the designed controller is exemplified by a numerical example.

Synchronous hybrid transport network design

Delay,as an inevitable real-world phenomenon,is usually ignored in transport network design.A model of urban hybrid transport system with stochastic delay was created on the basis of the idealized public transport system design.After formulating the total trip time cost composed of accessing time in the sub-region of the city,waiting time at the public transport station,and in-vehicle time in the public transit network,the analytical properties of the total trip time cost function were investigated.The results show that in the urban hybrid transport network design,the total trip time cost reaches its approximate minimum in a δ-neighbourhood of buffer time of 1.5 min,and that through modelling optimal delay in hybrid transport system,the maximal synchronization can be achieved and operational efficiency and passenger satisfaction can be improved.The proposed modelling and analytical investigations are attempts to contribute to more realistic modelling of future idealized public transport system that involves more practical constraints.