Existence and Global Exponential Stability of Almost Periodic Solution for Cellular Neural Networks With Variable Coefficients and Time-Varying Delays

In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.

Global Exponential Stability and Global Convergence in Finite Time of Delayed Neural Networks With Infinite Gain

This paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity, while the delay accounts for the finite switching speed of the neuron amplifiers, or the finite signal propagation speed. It is known that the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability. The goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay. More precisely, conditions are given under which there is a unique equilibrium point of the neural network, which is globally exponentially stable for the states, with a known convergence rate. The conditions are easily testable and independent of the delay. Moreover, global convergence in finite time of the state and output is investigated. In doing so, new interesting dynamical phenomena are highlighted with respect to the case without delay, which make the study of convergence in finite time significantly more difficult. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations but without delays.

A Delayed Neural Network for Solving Linear Projection Equations and its Analysis

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.

Global Asymptotic Stability Analysis of Bidirectional Associative Memory Neural Networks With Time Delays

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

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.

Global eponential stability of cellular neural networks with time-varying coefficients and delays

In this paper, a class of cellular neural networks with time-varying coefficients and delays is considered. By constructing a suitable Liapunov functional and utilizing the technique of matrix analysis, some new sufficient conditions on the global exponential stability of solutions are obtained. The results obtained in this paper improve and extend some of the previous results.

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

This paper derives a new sufficient condition for the exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a Lyapunov-Krasovskii functional and using Linear Matrix Inequality (LMI) approach. This result establishes a relation between the delay time and the parameters of the network. The result is also compared with the most recent result derived in the literature.

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.

Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays

In this paper, the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated. Without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions, Halanay-type inequalities (which are different from the approach of constructing Lyapunov functionals) are employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Our results are less conservative and restrictive than previously known results.