Bonan Huang

Novel synchronization analysis for complex networks with hybrid coupling by handling multitude Kronecker product terms

This paper is concerned with the problem of global synchronization for complex networks with hybrid coupling. An innovative approach is proposed to develop delay-dependent criteria for the system, which makes use of many relaxed information to construct Lyapunov functional, and employs an integral equation method and matrix expansion method to handle multitude Kronecker product terms. The method in this paper increases the number of arbitrary matrix, and alleviates the requirements of the positive definiteness of the matrix which should be considered in many existing references. This leads to significant improvement in the performance of the synchronization results. Finally, a chaotic synchronization example is provided to show the effectiveness of the proposed results.

Synchronization analysis for static neural networks with hybrid couplings and time delays

Abstract This paper deals with the synchronization problem for delayed static neural networks with hybrid couplings. When the static neural networks are affected by hybrid couplings, it is hard to deal with a large number of highly interconnected dynamical units in such a complex system. In order to solve this complicated problem, a new method is proposed to deal with the Kronecker product, and to make the synchronization problem to be easily analyzed. Further, based on the obtained result, by using the augmented Lyapunov–Krasovskii functional (LKF) method, multitude Kronecker product terms can be handled, which can introduce more relaxed conditions by employing the new type of augmented matrices with the Kronecker product operation. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed synchronization scheme.

Synchronization criteria and pinning control for complex networks with multiple delays

By linearizing complex networks with multiple coupling delays to some time-delayed subsystems, for the first time, some new criterions are given to ensure the global synchronization of the system with multiple delays. Then, based on the proposed criterions and Lyapunov stability theory, pinning control schemes for this system are developed to achieve global synchronization. The obtained conditions are expressed within the framework of linear matrix inequalities and can be easily checked in practice. Finally, several numerical examples are provided to show the effectiveness of the proposed results.

Pinning Synchronization for a General Complex Networks with Multiple Time-Varying Coupling Delays

This paper investigates the problem of pinning synchronization for a general complex networks with multiple time-varying coupling delays by using Lyapunov functional method. Firstly, we design a controller to keep the given system synchronized, and provide a simple approximate formula to estimate the detailed pinning synchronization states. Furthermore, by using the same method, an adaptive pinning control scheme is developed to achieve global synchronization, and the adaptive pinning controllers are simpler than some traditional controllers. Moreover, the presented results can also be applied to the system with single time delay, and the coupling-configuration matrices are not necessarily symmetric. Finally, numerical examples are given to show the effectiveness of the proposed methods.

New global synchronization analysis for complex networks with coupling delay based on a useful inequality

This paper is concerned with the problem of global synchronization for a general complex networks. Based on a useful inequality and Kronecker product technique, a new criterion is obtained, which has fewer unknown variables and is a significant improvement in the performance. Synchronization criteria are derived by some new mathematical skills and Schur complement. The result is expressed by linear matrix inequalities, which can be easily computed and checked in practice. Finally, numerical examples will be used to show the effectiveness of the obtained result.

Robust synchronization analysis for static delayed neural networks with nonlinear hybrid coupling

Abstract In this paper, the robust synchronization for static neural networks with nonlinear coupling and time-varying delay is studied. By constructing the appropriate augmented Lyapunov–Krasovskii functional, utilizing the theory of Kronecker product and the linear matrix inequality technique, we obtain the delay-dependent synchronization conditions which ensure the nonlinear coupled static neural networks with uncertainties in coupling matrices terms robust synchronization. The robust synchronization problem for the nonlinear hybrid coupled static delayed neural networks is first time investigated in this paper. At last, numerical example is provided to illustrate the effectiveness of the proposed results.

New results for neutral-type delayed projection neural network to solve linear variational inequalities

Recently, a neutral-type delayed projection neural network (NDPNN) was developed for solving variational inequality problems. This paper addresses the global stability and convergence of the NDPNN and presents new results for it to solve linear variational inequality (LVI). Compared with existing convergence results for neural networks to solve LVI, our results do not require the LVI that is monotone so as to guarantee the NDPNN that can solve a class of non-monotone LVI. All the results are expressed in terms of linear matrix inequalities, which can be easily checked. Simulation examples demonstrate the effectiveness of the obtained results.

A new result for projection neural networks to solve linear variational inequalities and related optimization problems

In recent years, a projection neural network was proposed for solving linear variational inequality (LVI) problems and related optimization problems, which required the monotonicity of LVI to guarantee its convergence to the optimal solution. In this paper, we present a new result on the global exponential convergence of the projection neural network. Unlike existing convergence results for the projection neural network, our main result does not assume the monotonicity of LVI problems. Therefore, the projection neural network can be further guaranteed to solve a class of non-monotone LVI and non-convex optimization problems. Numerical examples illustrate the effectiveness of the obtained result.

A projection neural network with mixed delays for solving linear variational inequality

This paper presents a projection neural network with discrete delays and distributed delays (i.e. mixed delays) for solving linear variational inequality (LVI). By the Lyapunov theory and the linear matrix inequality (LMI) approach, the neural network is proved to be globally exponentially convergent to the solution of LVI. Compared with existing neural networks for solving LVI, the proposed one features the ability of solving a class of non-monotone LVI. One numerical example is provided to illustrate the effectiveness and the satisfactory performance of the neural network.

Synchronization analysis for coupled static neural networks with stochastic disturbance and interval time-varying delay

This paper is concerned with the stochastic synchronization problem of coupled static neural networks with interval time-varying delays. By employing the augmented Lyapunov–Krasovskii method and a new method to deal with the Kronecker product, a delay-dependent synchronization criterion is established to guarantee the global asymptotical mean-square synchronization of the addressed delayed networks with stochastic disturbances. The obtained result is formulated in terms of linear matrix inequalities which can be easily checked. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.