Exponential Synchronization Of Complex Networks Research Articles

Global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling

This article investigates global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling (RDDCCNs). Some restrictions on the coupling configuration matrix and time-varying delays are removed. By constructing comparison functions, utilizing analytic method and inequality techniques, a criterion for exponential synchronization of RDDCCNs is attained under adaptive intermittent control. A corresponding outcome without RDs is also acquired. At last, two simulations are proposed to illustrate validity of the obtained criteria.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Exponential synchronization of complex networks via feedback control and periodically intermittent noise

In complex networks, asymptotic properties play an important role in modeling, analysis and design in both aspects of theory and practice. In this paper, our focus is on exponential synchronization for a class of complex networks. Under certain conditions, a feedback control and stochastic periodically intermittent noise are designed to synchronize the networks. Such synchronization scheme needs less control energy due to the usage of the intermittent noise. The threshold of intermittent rate for synchronization scheme is derived. Moreover, the noise states are observed in discrete-time mode, which reduces the complexity and the computation burden for continuous observations. The observation supremum is obtained by solving a transcendental equation. Finally, a simulation example is provided, and the comparison results with some existing methods illustrate the effectiveness and advantages of the proposed new design strategy.

Exponential Synchronization of Complex Networks: An Intermittent Adaptive Event-Triggered Control Strategy

This paper investigates the exponential synchronization (ES) problem for complex networks (CNs) under an intermittent adaptive event-triggered control (IAE-TC) strategy which is based on dynamic IAE-TC during the control activation intervals. In this control mechanism, the intermittent controller has adaptability to the evolution results of the controlled networks and is activated only when the event-triggered condition is violated. Then, by employing this kind of control strategy and the Lyapunov method, some sufficient conditions are proposed to achieve the ES of CNs and it is proven that the Zeno behavior can be eliminated. Besides, an application about the islanded microgrid system and some numerical simulations are provided to verify the effectiveness of the derived theoretical results. Moreover, in the numerical simulations, it is shown that the dynamic IAE-TC strategy can decrease the number of event-triggered instants more availably than the static one.

Stochastic synchronization of complex networks via aperiodically intermittent noise

This paper focuses on exponential synchronization of complex networks controlled by aperiodically intermittent noise with time delays. An aperiodically intermittent controller is designed to synchronize complex networks and the interval of intermittent rate is derived. Delay observations on the state of noise are made and the upper bound of time delays is obtained. A sufficient condition for exponential synchronization of the underlying systems is derived. Moreover, the auxiliary networks without time delays are introduced and the sufficient criterion for stochastic synchronization of the networks is also obtained. The comparison principle plays a significant role in synchronizing complex networks in this paper. An example is given to demonstrate the feasibility and effectiveness of the new approaches.

Synchronization of complex networks with impulsive control involving stabilizing delay

This paper mainly investigates the globally exponential synchronization of complex networks (CNs) via delayed impulsive control, where the stabilizing effects of time-delay in impulses are fully considered. Based on Lyapunov method and average dwell-time (ADT) approach, sufficient conditions are proposed to deal with the synchronization problem of CNs. Furthermore, the robustness of CNs with parametric uncertainties is discussed. Finally, two examples are given to illustrate the effectiveness of the theoretical results.

Exponential synchronization of complex networks with continuous dynamics and Boolean mechanism

Abstract In this paper, we investigate a new model of complex networks with continuous dynamics and Boolean mechanism. Firstly, we give the expression of this new class of complex networks. Next, based on semi-tensor product technique and Lyapunov function, a criterion of globally exponential synchronization for the complex networks is given. Further, we take impulsive effects into consideration and establish corresponding conditions of globally exponential synchronization. Finally, examples are simulated to illustrate the effectiveness of the main obtained results.

Event-based exponential synchronization of complex networks.

In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed event-triggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.

Exponentially impulsive projective and lag synchronization between uncertain complex networks

This paper is concerned with exponentially projective and lag synchronization between general complex networks via impulsive control. Presented general complex networks are uncertain with time-varying delays in both coupled and uncoupled terms. Different dynamics for each node is taken into account in order to cover the practical needs. Based on the impulsive control theory, the global exponential synchronization of complex networks is analyzed and some new sufficient conditions are derived. Moreover, two numerical examples are presented to demonstrate the effectiveness of the proposed method, first one is devoted to synchronization of networks with self-excited attractor and second one is for networks with hidden attractor.

Exponential synchronization of complex networks of linear systems and nonlinear oscillators: a unified analysis.

A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.

Pinning exponential synchronization of complex networks via event-triggered communication with combinational measurements

In this paper, we consider the pinning exponential synchronization of complex networks via event-triggered communication. By using the combinational measurements, two classes of event triggers are designed, one depends on continuous communications between the agents, the other avoids the continuous communications. The controller updates when triggering function reaches certain threshold. For such classes of two event triggers, the exponential synchronization as well as the convergence rate of the controlled complex networks are studied, respectively, by employing the M-matrix theory, algebraic graph theory and the Lyapunov method. Two simulation examples are provided to illustrate the effectiveness of the proposed two classes of event triggering strategies. It is noteworthy that the event trigger with combinational measurements avoids decoupling the actual state of the nodes, which is more effective than the error-based event trigger.

Stochastic Synchronization of Complex Networks With Mixed Impulses

In this paper, stochastic synchronization is studied for complex networks with delayed coupling and mixed impulses. Mixed impulses are composed of desynchronizing and synchronizing impulses. The delayed coupling term involves transmission delay and self-feedback delay. By using the average impulsive interval approach and the comparison principle, several conditions are derived to guarantee that exponential synchronization of complex networks is achieved in the mean square. The derived conditions are closely related to the impulsive strengths, the frequency of impulse occurrence, and the coupling structure of complex networks. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.

Exponential Synchronization of Complex Networks With Finite Distributed Delays Coupling

In this paper, the exponential synchronization for a class of complex networks with finite distributed delays coupling is studied via periodically intermittent control. Some novel and useful criteria are derived by utilizing a different technique compared with some correspondingly previous results. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural networks with distributed delays are obtained. Furthermore, a feasible region of the control parameters is derived for the realization of exponential synchronization. It is worth noting that the synchronized state in this paper is not an isolated node but a non-decoupled state, in which the inner coupling matrix and the degree of the nodes play a central role. Additionally, the traditional assumptions on control width, non-control width, and discrete delays are removed in our results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes

In this Letter, exponential synchronization of a complex network with nonidentical time-delayed dynamical nodes is considered. Two effective control schemes are proposed to drive the network to synchronize globally exponentially onto any smooth goal dynamics. By applying open-loop control to all nodes and adding some intermittent controllers to partial nodes, some simple criteria for exponential synchronization of such network are established. Meanwhile, a pinning scheme deciding which nodes need to be pinned and a simply approximate formula for estimating the least number of pinned nodes are also provided. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network with nonidentical time-delayed dynamical nodes, and an estimate of the upper bound of impulsive intervals ensuring global exponential stability of the synchronization process is also given. Numerical simulations are presented finally to demonstrate the effectiveness of the theoretical results.

Exponential synchronization of complex networks with Markovian jump and mixed delays

In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.