Cluster Synchronization Criteria Research Articles

Event-triggered impulsive cluster synchronization of coupled reaction–diffusion neural networks and its application to image encryption

This paper investigates the cluster synchronization of coupled neural networks with reaction–diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Adaptive dynamic event-triggered cluster synchronization in an array of coupled neural networks subject to cyber-attacks

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results.

Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control.

In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.

Cluster Synchronization of Two-Layer Networks via Aperiodically Intermittent Pinning Control

As is well known, complex networks in reality are usually interconnected. To describe the interconnected networks, multiplex networks were presented recently. In this brief, an aperiodically intermittent pinning control scheme is put forward to realize cluster exponential synchronization in a two-layer (leader-follower) network with multi-links and time-varying delays. Based on the principle of intermittent control and Lasalle invariant principle, some criteria for cluster synchronization are deduced by theoretical analysis. Numerical simulations are provided to verify the effectiveness of the proposed scheme. In comparison with the previous methods, our model better describes the real-world networks and our control effectively reduces the control cost.

Finite-time cluster synchronization of coupled dynamical systems with impulsive effects

In our paper, the finite-time cluster synchronization problem is investigated for the coupled dynamical systems in networks. Based on impulsive differential equation theory and differential inequality method, two novel Lyapunov-based finite-time stability results are proposed and be used to obtain the finite-time cluster synchronization criteria for the coupled dynamical systems with synchronization and desynchronization impulsive effects, respectively. The settling time with respect to the average impulsive interval is estimated according to the sufficient synchronization conditions. It is illustrated that the introduced settling time is not only dependent on the initial conditions, but also dependent on the impulsive effects. Compared with the results without stabilizing impulses, the attractive domain of the finite-time stability can be enlarged by adding impulsive control input. Conversely, the smaller attractive domain can be obtained when the original system is subject to the destabilizing impulses. By using our criteria, the continuous feedback control can always be designed to finite-time stabilize the unstable impulsive system. Several existed results are extended and improved in the literature. Finally, typical numerical examples involving the large-scale complex network are outlined to exemplify the availability of the impulsive control and continuous feedback control, respectively.

Cluster synchronization of two-layer nonlinearly coupled multiplex networks with multi-links and time-delays

The cluster synchronization problem of two-layer nonlinearly coupled multiplex networks with multi-links and time-delays is investigated in this paper. The main feature of this literature can be summarized as follows: (i) introduce a double-layer multiplex networks composed of many pairs of matching leaders’ subnets and followers’ subnets with multi-links, which gives much more chances for these leaders to transmit information to their matching followers; (ii) configure the multi-links with nonlinear coupling and time-varying delays; (iii) give out the designed pinning scheme that the nodes with low degrees are in need of applying controllers first and some appropriate adaptive update laws, which are used for processing the unknown feedback factors between the pinned nodes and their leaders; (iv) free from the general constraints on the node sizes in each subnet pairs. In view of Lyapunov stability theory of delayed dynamical systems and with the design of an adaptive pinning strategy, some cluster synchronization criteria of two-layer multi-linked multiplex network are proposed. Both theoretical analysis and numerical simulations demonstrate that the proposed adaptive pinning scheme is feasible and effective.

Fixed-time cluster synchronization in directed community networks with diverse coupling and different-order nodes

In this paper, fixed-time cluster synchronization of directed community networks (DCNs) with diverse coupling and different-order nodes is explored. For the DCN model, the inherent dynamics and state dimensions of the nodes in different communities can be nonidentical, and moreover, the interactive nodes can differ in their types of connections in different communities and the connections between any pair of different communities can be nonidentical as well. Two types of control strategies, state feedback control and adaptive feedback control, are adopted to force such DCNs to realize cluster synchronization in fixed-time. By utilizing reduction to absurdity, some sufficient conditions ensuring the fixed-time cluster synchronization are derived for the proposed two control schemes. Moreover, it is revealed theoretically that our estimated settling time is more precise and less conservative than that presented in the previous researches. Finally, the validity of the obtained fixed-time cluster synchronization criteria is verified via numerical simulations.

Finite-time cluster synchronization for time-varying delayed complex dynamical networks via hybrid control

Throughout this article, the conundrum on finite-time cluster synchronization is investigated for time-varying delayed complex dynamical networks using a kind of new hybrid control scheme. In the light of Lyapunov stability theorem and finite-time control theory, the finite-time cluster synchronization criteria can be achieved. Besides, we introduce the distinction between cluster synchronization and complete synchronization, which is how to select the controlling nodes. We discuss the differences among cluster synchronization with time-varying delays, complete synchronization with time-varying delays, cluster synchronization with a single delay, and cluster synchronization without delay, which is on constructing Lyapunov functional and designing the finite-time hybrid controllers. Finally, numerical simulations are presented to demonstrate the availability of the theoretical consequences.

Fixed-Time Cluster Synchronization of Discontinuous Directed Community Networks via Periodically or Aperiodically Switching Control

The fixed-time cluster synchronization problem for a class of directed community networks with linear couplings and discontinuous nodes is investigated in this paper. First, by means of reduction to absurdity and mathematical induction, two new and vital differential equalities are proposed and proved to study the fixed-time stability. Besides, by designing periodically switching controllers and aperiodically adaptive switching controllers, as well as using the theory of differential inclusions, some fixed-time cluster synchronization criteria are derived in which the settling time function is bounded for any initial values. Finally, the numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem.

New Cluster Synchronization Criteria for Markov Jump Coupled Neural Networks of Neutral-Type with Unknown Transition Rates

New Cluster Synchronization Criteria for Markov Jump Coupled Neural Networks of Neutral-Type with Unknown Transition Rates

Cluster oscillatory synchronization of networked Lagrangian systems with the distributed adaptive observers

This paper investigates cluster synchronization problem for uncertain networked Lagrangian systems with nonidentical oscillatory leaders. Firstly, in the case of positive couplings and in the case of positive and negative couplings, we propose two different distributed adaptive observers. Based on these adaptive observers, two adaptive controllers are developed. Then, some cluster synchronization criteria are given to ensure that the desired cluster synchronization scheme can be arrived. Due to introduction of these two adaptive observers, it is no longer necessary for each follower to obtain the frequency information of the corresponding leader system. Finally, the performance and effective of the provided controllers are verified by some numerical examples.

Adaptive exponential cluster synchronization in colored community networks via aperiodically intermittent pinning control

This paper investigates the problem of pinning cluster synchronization for colored community networks via adaptive aperiodically intermittent control. Firstly, a general colored community network model is proposed, where the isolated nodes can interact through different kinds of connections in different communities and the interactions between different pair of communities can also be different, and moreover, the nodes in different communities can have different state dimensions. Then, an adaptive aperiodically intermittent control strategy combined with pinning scheme is developed to realize cluster synchronization of such colored community network. By introducing a novel piecewise continuous auxiliary function, some globally exponential cluster synchronization criteria are rigorously derived according to Lyapunov stability theory and piecewise analysis approach. Based on the derived criteria, a guideline to illustrate which nodes in each community should be preferentially pinned is given. It is noted that the adaptive intermittent pinning control is aperiodic, in which both control width and control period are allowed to be variable. Finally, a numerical example is provided to show the effectiveness of the theoretical results obtained.

Exponential cluster synchronization in directed community networks via adaptive nonperiodically intermittent pinning control

In this paper, the problem of exponential cluster synchronization for a class of directed community networks is investigated via adaptive nonperiodically intermittent pinning control. By constructing a novel piecewise continuous Lyapunov function, some sufficient conditions to guarantee globally exponential cluster synchronization are derived. It is noted that the derived cluster synchronization criteria rely on the control rates, but not the control widths or the control periods, which facilitates the choice of the control periods in practical applications. A numerical example is finally presented to show the effectiveness of the obtained theoretical results.

Cluster Synchronization of Coupled Genetic Regulatory Networks With Delays via Aperiodically Adaptive Intermittent Control.

In this paper, we study the cluster synchronization of coupled genetic regulatory networks with time-varying delays via aperiodically adaptive intermittent control on some nodes. The network is intermittently coupled and the intra-cluster coupling strength is adaptively adjusted. The graph of the coupling topology of each cluster is only required to have a directed spanning tree. Two cases of delays are considered. In the first case, by using the switching Lyapunov-based function and Razumikhin-type technique, the cluster synchronization criterion is presented which indicates that the cluster synchronization is realized via the aperiodically adaptive intermittent control. The second case is investigated by using the switching Lyapunov functional. Both the cluster synchronization criteria are established by the Linear Matrix Inequalities (LMIs), the lower bound of the aperiodical time span, and the maximum uncontrolled ratio. It is shown that the results are applicable to both the situations that the upper bound of the delay is larger and smaller than the lower bound of the aperiodical coupling and control width. Numerical simulations are carried out to illustrate the theoretical results.

Adaptive finite-time control for overlapping cluster synchronization in coupled complex networks

In this paper, we address the overlapping cluster synchronization problem of coupled complex networks via adaptive finite-time control. Cluster synchronization indeed has been extensively addressed by various control strategies. The communities in the cluster-based networks always do not share nodes with each other but exchange messages. Then, according to natural community, we propose a new overlapping community model for the coupled complex network to remove the restriction on common community models. The community in our model contains two kinds of nodes: overlapped and non-overlapped nodes, which is different from the common cluster form explored in the synchronization processing. In addition, a new control strategy is expressly proposed to extract every inner cluster in the overlapped regions. Especially, a novel adaptive finite-time control strategy is also proposed to force every community to a desired trajectory in finite time. On the basis of finite time theory, sufficient cluster synchronization criteria are derived. Lastly, the effectiveness of analytical results is confirmed by a numerical example.

Pinning cluster synchronization of delayed complex dynamical networks with nonidentical nodes and impulsive effects

This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive control approach is proposed to achieve the exponential cluster synchronization of the considered network. By employing a time-dependent Lyapunov functional, less conservative cluster synchronization criteria are established in the form of linear matrix inequalities. Compared with the existing works, the constructed Lyapunov functional is related with impulse time sequence, which makes full use of the information on dynamical characteristic of synchronization error dynamics. Finally, a numerical example of typical chua’s system is given to illustrate the effectiveness and correctness of the theoretical results.

Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays

This investigation establishes the global cluster synchronization of complex networks with a community structure based on an iterative approach. The units comprising the network are described by differential equations, and can be non-autonomous and involve time delays. In addition, units in the different communities can be governed by different equations. The coupling configuration of the network is rather general. The coupling terms can be non-diffusive, nonlinear, asymmetric, and with heterogeneous coupling delays. Based on this approach, both delay-dependent and delay-independent criteria for global cluster synchronization are derived. We implement the present approach for a nonlinearly coupled neural network with heterogeneous coupling delays. Two numerical examples are given to show that neural networks can behave in a variety of new collective ways under the synchronization criteria. These examples also demonstrate that neural networks remain synchronized in spite of coupling delays between neurons across different communities; however, they may lose synchrony if the coupling delays between the neurons within the same community are too large, such that the synchronization criteria are violated.

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

In this paper, the problem of exponential cluster synchronization of general hybrid-coupled impulsive dynamical networks with internal delay and delayed coupling is investigated. A more general delayed coupling term including different transmission delay and self-feedback delay is taken into account. By using average impulsive interval approach and the analysis technique, some novel globally exponential cluster synchronization criteria are derived analytically. It is noted that the internal delay, transmission delay and self-feedback delay are all time-varying and can be different from each other, the inner connecting matrices are not demanded to be diagonal and the coupling matrices are not restricted to be symmetric or irreducible, more consistent with the realistic networks. Particularly, it is shown that the derived cluster synchronization criteria are simultaneously applicable for studying general delayed dynamical networks with synchronizing impulses or desynchronizing impulses. Numerical examples are finally given to illustrate the effectiveness of the obtained theoretical results.

Cluster Synchronization on Multiple Nonlinearly Coupled Dynamical Subnetworks of Complex Networks With Nonidentical Nodes.

In this paper, cluster synchronization on multiple nonlinearly coupled dynamical subnetworks of complex networks with nonidentical nodes and stochastic perturbations is studied. Based on the general leader-follower's model, an improved network structure model that consists of multiple pairs of matching subnetworks, each of which includes a leaders' subnetwork and a followers' subnetwork, is proposed. Moreover, the dynamical behaviors of the nodes belonging to the same pair of matching subnetworks are identical, while the ones belonging to different pairs of unmatched subnetworks are nonidentical. In this new setting, the aim is to design some suitable adaptive pinning controllers on the chosen nodes of each followers' subnetwork, such that the nodes in each subnetwork can be exponentially synchronized onto their reference state. Then, some cluster synchronization criteria for multiple nonlinearly coupled dynamical subnetworks of complex networks are established, and a pinning control scheme that the nodes with very large or low degrees are good candidates for applying pinning controllers is presented. Suitable adaptive update laws are used to deal with the unknown feedback gains between the pinned nodes and their leaders. Finally, several numerical simulations are given to demonstrate the effectiveness and applicability of the proposed approach.

Adaptive pinning control of cluster synchronization in complex networks with Lurie-type nonlinear dynamics

In this paper, cluster synchronization problem is investigated for a kind of complex dynamical networks with Lurie-type non-linear dynamics. With the aid of a local update law, a pinning adaptive control strategy is proposed to solve the cluster synchronization problem of the networks. Some simple criteria for cluster synchronization are presented for the networks with external disturbances and time delays. Firstly, sufficient conditions are established to realize cluster synchronization of the networks without disturbances and delays. Then, the cluster synchronization problem of the networks with external disturbances is considered. Finally, the cluster synchronization in the networks with time-varying delays is further studied. Numerical examples are given to verify and illustrate the theoretical results.