Xianyun Xu

Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay

Abstract In this paper, we study the global asymptotic stability of fractional-order BAM neural networks. We take both time delay and impulsive effects into consideration. Based on Lyapunov stability theorem, fractional Barbalat’s lemma and Razumikhin-type stability theorem, some stability conditions that are independent of the form of specific delays can be obtained. At last, two illustrative examples are given to show the independence of the obtained two main results and to show the effectiveness of the obtained results.

A new neural network for solving quadratic programming problems with equality and inequality constraints

A new neural network is proposed in this paper for solving quadratic programming problems with equality and inequality constraints. Comparing with the existing neural networks for solving such problems, the proposed neural network has fewer neurons and an one-layer architecture. The proposed neural network is proven to be global convergence. Furthermore, illustrative examples are given to show the effectiveness of the proposed neural network.

The impulsive control of the projective synchronization in the drive-response dynamical networks with coupling delay

In this paper, we study the impulsive control of the projective synchronization in the drive-response dynamical networks with coupling delay, where the drive system is a partially linear chaotic system and the response system is a delay-coupled dynamical network The method also allows us to arbitrarily amplify or reduce the scale of the dynamics of the response network through the impulsive control Numerical simulations are provided to demonstrate the effectiveness of the proposed control method.

A generalized neural network for solving a class of minimax optimization problems with linear constraints

Abstract In this paper, a generalized neural network was proposed based on projection method and differential inclusions, which is contributed to solve a class of minimax optimization problems with linear constraints. It is proved that the solution trajectory can converge to the feasible region in the finite time when the initial point is not in the feasible region. Once the solution trajectory reaches the feasible region, it will stay therein thereafter. In addition, we investigate the global convergence and exponential convergence. Furthermore, three illustrative examples are given to show the efficiency of the proposed neural network.

Sampled-data state estimation for neural networks of neutral type

In this paper, the sampled-data state estimation is investigated for a class of neural networks of neutral type. By employing a suitable Lyapunov functional, a delay-dependent criterion is established to guarantee the existence of the sampled-data estimator. The estimator gain matrix can be obtained by solving linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the proposed method.

Convergence of the projection-based generalized neural network and the application to nonsmooth optimization problems

This paper introduces a projection-based generalized neural network, which can be used to solve a class of nonsmooth convex optimization problems It generalizes the existing projection neural networks for solving the optimization problems In addition, the existence and convergence of the solution for the generalized neural networks are proved Moreover, we discuss the application to nonsmooth convex optimization problems And two illustrative examples are given to show the efficiency of the theoretical results.

Synchronization of complex dynamical networks via sampled-data control: A threshold function event-triggered method

The synchronization problem of a general complex dynamical networks is studied in this paper. Sampled-data feedback controllers with event triggered mechanism are designed to synchronize the complex network. The event in this paper is formed as a kind of monotone non-increasing threshold function. According to Lyapunov stability theory, quasi-synchronization can be reached, and the error level is related with some parameters of selected threshold function. Furthermore, under some appropriate parameters, the completed-synchronization can be guaranteed. Some examples are given to illustrate the effectiveness of the proposed to support theoretical results.

A New Sampled-Data State Estimator for Neural Networks of Neutral-Type with Time-Varying Delays

This paper is concerned with the sampled-data state estimation problem for neural networks of neutral-type with time-varying delays. A new state estimator was designed based on the sampled measurements. The sufficient condition for the existence of state estimator is derived by using the Lyapunov functional method. A numerical example is given to show the effectiveness of the proposed estimator.

Existence and Uniqueness of Almost Automorphic Solutions to Cohen-Grossberg Neural Networks with Delays

The almost automorphic solution is a generalization of the almost periodic solution. In this paper, the almost automorphic solutions of Cohen-Grossberg neural networks with delays are considered. Using the semi-discretization method and the contraction mapping principle, some sufficient conditions are obtained to ensure the existence and the uniqueness of almost automorphic solutions to Cohen-Grossberg neural networks with delays.

Existence of periodic solution for competitive neural networks with time-varying and distributed delays on time scales

In this paper, under the condition without assuming the boundedness of the activation functions, the competitive neural networks with time-varying and distributed delays are studied. By means of contraction mapping principle, the existence and uniqueness of periodic solution are investigated on time scales.