Adaptive pinning cluster synchronization of a stochastic reaction-diffusion complex network.

This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction-diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction-diffusion neural networks with stochastic noise and Markovian switching are given.

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks.

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Pinning bipartite synchronization for inertial coupled delayed neural networks with signed digraph via non-reduced order method.

The study investigates bipartite synchronization of inertial coupled delayed neural networks (ICDNNs) with signed digraph by non-reduced order method and pinning control. The second-order CDNNs will not be converted into a first-order differential system by introducing variable substitution. Instead, a novel Lyapunov-Krasovskii functional is proposed which depends on the topology of the ICDNNs. Some sufficient conditions for linear matrix inequalities (LMI) are derived to realize bipartite synchronization, which is based on matrix decomposition theory and Barbalat Lemma in strongly connected signed networks. And then, M-matrix theory is utilized to generalize the results to networks containing directed spanning trees. Finally, two examples are used to verify the validity of the derived theoretical results.

Spacial sampled-data control for H∞ output synchronization of directed coupled reaction-diffusion neural networks with mixed delays.

This work investigates the H∞ output synchronization (HOS) of the directed coupled reaction-diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet-Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.

Synchronization of hybrid coupled reaction-diffusion neural networks with time delays via generalized intermittent control with spacial sampled-data.

The exponential synchronization of hybrid coupled reaction-diffusion neural networks with time delays is discussed in this article. At first, a generalized intermittent control with spacial sampled-data is introduced, which is intermittent in time and data sampling in space. This type of control strategy not only can unify the traditional periodic intermittent control and the aperiodic case, but also can lower the update rate of the controller in both temporal and spatial domains. Next, based on the designed control protocol and the Lyapunov-Krasovskii functional approach, some novel and readily verified criteria are established to guarantee the exponential synchronization of the considered networks. These criteria depend on the diffusion coefficients, coupled strengths, time delays as well as control parameters. Finally, the effectiveness of the proposed control strategy is shown by a numerical example.