Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks

This paper is concerned with the finite-time synchronization (FTS) issue of switched coupled neural networks with discontinuous or continuous activations. Based on the framework of nonsmooth analysis, some discontinuous or continuous controllers are designed to force the coupled networks to synchronize to an isolated neural network. Some sufficient conditions are derived to ensure the FTS by utilizing the well-known finite-time stability theorem for nonlinear systems. Compared with the previous literatures, such synchronization objective will be realized when the activations and the controllers are both discontinuous. The obtained results in this paper include and extend the earlier works on the synchronization issue of coupled networks with Lipschitz continuous conditions. Moreover, an upper bound of the settling time for synchronization is estimated. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays

In this paper, a class of recurrent neural networks with discrete and continuously distributed delays is considered. Sufficient conditions for the existence, uniqueness, and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations. The proposed method, which differs from the existing results in the literature, shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent. Two numerical examples and their computer simulations are offered to show the effectiveness of our new results.

Convergence dynamics of stochastic Cohen-Grossberg neural networks with unbounded distributed delays

This paper addresses the issue of the convergence dynamics of stochastic Cohen-Grossberg neural networks (SCGNNs) with white noise, whose state variables are described by stochastic nonlinear integro-differential equations. With the help of Lyapunov functional, semi-martingale theory, and inequality techniques, some novel sufficient conditions on pth moment exponential stability and almost sure exponential stability for SCGNN are given. Furthermore, as byproducts of our main results, some sufficient conditions for checking stability of deterministic CGNNs with unbounded distributed delays have been established. Especially, even when the spectral radius of the coefficient matrix is greater than 1, in some cases our theory is also effective.

On the global stability of time delayed CNNs

The objective of this paper is the concise presentation of the most important and recent lemmas and theorems associated with the global asymptotic and exponential stability of the equilibrium point of time delayed cellular neural networks. For each theorem a short proof is given, so that the reader can understand its features and its relationships to other theorems. In the last section, the presented theorems are grouped according to their characteristics and the way they relate to one another, and some of them are demonstrated, in order to draw conclusions about their use.

Local synchronization of one-to-one coupled neural networks with discontinuous activations

In this paper, local synchronization is considered for coupled delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution and in the sense of generalized derivative, a novel sufficient condition is obtained to ensure the synchronization based on the Lyapunov exponent and the detailed analysis in Danca (Int J Bifurcat Chaos 12(8):1813-1826, 2002; Chaos Solitons Fractals 22:605-612, 2004). Simulation results are given to illustrate the theoretical results.

Global Asymptotic Stability of Delayed Cellular Neural Networks

A new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented. The obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior-point algorithm. A numerical example is used to show the effectiveness of the obtained result.

Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli

This paper presents new theoretical results on the global exponential stability of recurrent neural networks with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. As special cases, the Hopfield neural network and the cellular neural network are examined in detail. In addition, it is shown that criteria herein, if partially satisfied, can still be used in combination with existing stability conditions. Simulation results are also discussed in two illustrative examples.

Advanced fuzzy cellular neural network: application to CT liver images

OBJECTIVE

To achieve better boundary integrities and recall accuracies for segmented liver images, use of the advanced fuzzy cellular neural network (AFCNN), as a variant of the fuzzy cellular neural network (FCNN), is proposed to effectively segment CT liver images.

MATERIALS AND METHODS

In order to better utilize relevant contour and gray information from liver images, we have improved the FCNN [Wang S, Wang M. A new algorithm NDA based on fuzzy cellular neural networks for white blood cell detection. IEEE Trans Inform Technol Biomed, in press], which proved to be very effective for the segmentation of microscopic white blood cell images, to create the novel neural network, AFCNN. Its convergent property and global stability are proved. Based on the FCNN-based NDA algorithm [Wang S, Wang M. A new algorithm NDA based on fuzzy cellular neural networks for white blood cell detection. IEEE Trans Inform Technol Biomed, in press], we developed the AFCNN-based NDA algorithm, which we used to segment 5 CT liver images. For comparison, we also segmented the same 5 CT liver images using the FCNN-based NDA algorithm.

RESULTS AND CONCLUSION

: AFCNN has distinct advantages over FCNN in both boundary integrity and recall accuracy. In particular, the performance index Binary_rate is generally much higher for AFCNN than for FCNN when applied to CT liver images.

An Improved Global Asymptotic Stability Criterion for Delayed Cellular Neural Networks

A new Lyapunov-Krasovskii functional is constructed for delayed cellular neural networks, and the S-procedure is employed to handle the nonlinearities. An improved global asymptotic stability criterion is also derived that is a generalization of, and an improvement over, previous results. Numerical examples demonstrate the effectiveness of the criterion.

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems.

Boundedness and stability for nonautonomous cellular neural networks with delay

In this paper, a class of nonautonomous cellular neural networks is studied. By constructing a suitable Liapunov functional, applying the boundedness theorem for general functional-differential equations and the Banach fixed point theorem, a series of new criteria are obtained on the boundedness, global exponential stability, and existence of periodic solutions.

Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays

This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapunov function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.

Absolutely exponential stability of a class of neural networks with unbounded delay

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of neural networks with partially Lipschitz continuous activation functions are investigated. The neural networks contain both variable and unbounded delays. Using the matrix property, a necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions and nonlinear integro-differential inequalities involving both variable delays and unbounded delay, using M-matrix theory, sufficient conditions for absolutely exponential stability are obtained.