Matrix analysis
Numerical solutions of stochastic differential delay equations under local Lipschitz condition
Journal of Computational and Applied Mathematics
Pattern recognition via synchronization in phase-locked loop neural networks
IEEE Transactions on Neural Networks
Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Brief paper: A unified synchronization criterion for impulsive dynamical networks
Automatica (Journal of IFAC)
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Original article: Pinning synchronization of linearly coupled delayed neural networks
Mathematics and Computers in Simulation
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Pinning stabilization problem of linearly coupled stochastic neural networks (LCSNNs) is studied in this paper. A minimum number of controllers are used to force the LCSNNs to the desired equilibrium point by fully utilizing the structure of the network. In order to pinning control the LCSNNs to a certain desired state, only one controller is required for strongly connected network topology, and M controllers, which will be shown to be the minimum number, are needed for LCSNNs with M-reducible coupling matrix. The isolate node of the LCSNNs can be stable, periodic, or even chaotic. The coupling Laplacian matrix of the LCSNNs can be symmetric irreducible, asymmetric irreducible, or M-reducible, which means that the network topology can be strongly connected, weakly connected, or even unconnected. There is no constraint on the network topology. Some criteria are derived to judge whether the LCSNNs can be controlled in mean square by using designed controllers. The given criteria are expressed in terms of strict linear matrix inequalities, which can be easily checked by resorting to recently developed algorithm. Moreover, numerical examples including small-world and scale-free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems.