https://bura.brunel.ac.uk/bitstream/2438/4950/3/Fulltext.pdf

Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.

Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic stability are discussed for a general class of recurrent neural networks with time-varying delays and Lipschitz continuous activation functions. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural networks as its special cases. Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals. The new criteria do not require the activation functions to be differentiable, bounded or monotone nondecreasing and the connection weight matrices to be symmetric. Some stability results from previous works are extended and improved. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.

Global asymptotic stability of a general class of recurrent neural networks with time-varying delays

Stability problems of continuous-time recurrent neural networks have been extensively studied, and many papers have been published in the literature The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time recurrent neural networks, including Hopfield neural networks, Cohen-Grossberg neural networks, and related models Since time delay is inevitable in practice, stability results of recurrent neural networks with different classes of time delays are reviewed in detail For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in recurrent neural networks are summarized The relationship among stability results in different forms, such as algebraic inequality forms, \(M\) -matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared Some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed Concluding remarks and future directions of stability analysis of recurrent neural networks are given

https://romisatriawahono.net/lecture/rm/survey/machine%20learning/Zhang%20-%20Stability%20Analysis%20of%20Continuous-Time%20Recurrent%20Neural%20Networks%20-2014.pdf

A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks

In this paper, a sufficient condition is presented for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks (DCNN's). This condition imposes constraints on the feedback matrices independently of the delay parameter. This result is also discussed from the point of view of its relationship to earlier results.

On the global asymptotic stability of delayed cellular neural networks

In this paper, the author derives several sufficient conditions for the asymptotic stability of delayed neural networks. These conditions ensure the asymptotic stability of the equilibrium point of a delayed neural network independently of the delay parameter. The results obtained impose constraint conditions on the interconnection matrix of the neural system. These results are also compared with the earlier results derived in the literature.

Stability analysis of delayed neural networks

In this paper, a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks (DCNNs). This condition imposes constraints on the feedback and delayed feedback matrices of a DCNN independently of the delay parameter. This result is also compared with the previous results derived in the literature.

Sabri Arik

Papers

On the global asymptotic stability of delayed cellular neural networks

Stability analysis of delayed neural networks

An analysis of global asymptotic stability of delayed cellular neural networks

Global asymptotic stability of a larger class of neural networks with constant time delay

An analysis of exponential stability of delayed neural networks with time varying delays