New proof on exponential convergence for cellular neural networks with time-varying delays

Abstract

In this paper, we deal with a class of cellular neural networks with time-varying delays. Applying differential inequality strategies without assuming the boundedness conditions on the activation functions, we obtain a new sufficient condition that ensures that all solutions of the considered neural networks converge exponentially to the zero equilibrium point. We give an example to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Tang (Appl. Math. Lett. 21:872-876, 2008).

Synchronization on the non-autonomous cellular neural networks with time delays

“…In addition, an example and its numerical simulations are provided to validate the correctness of the theoretical results in this paper. In comparison to previous results presented in [21]- [28], results of this paper are less conservative and more general. Moreover, the theoretical results in this paper can be seen as a complement and an extension to the previous works [21]- [28].…”

“…But the intrinsic parameters of the non-autonomous NNs are variables and have input effect. Up to now, the majority of existing results are devoted to the autonomous NNs [12]- [26], and there are few papers considered the non-autonomous NNs [27,28]. In [27,28], the authors considered the following non-autonomous cellular neural networks(CNNs) with time variable delays and infinite delayṡ…”

“…The authors obtained some sufficient conditions on the exponential convergence for system (1.1) by using the differential inequality strategies. But, in [27,28], the authors did not consider the estimation of exponential convergent rate. On the other hand, in the process of investigating neural networks, the estimate of the convergent rate of the synchronization is one of the major concerns and useful for studying the synchronization of chaotic systems [22].…”

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

“…Here we do not assume that f j are Lipschitz and hypothesis (H1) only implies the continuity of f j at u = 0. Condition (H1) is assumed in [10] for discrete-time models and in [32] for continuous-time models. The most famous activation functions used in neural networks, such as linear ReLu (rectified linear unit), leaky ReLu, sigmoid, and tanh (hyperbolic tangent), verify hypothesis (H1).…”

General decay synchronization stability on the nonautonomous BAM recurrent neural networks with delays

“…Therefore, a nonautonomous scenario is necessary for NNs models, making it worthy to study the NNs models in a nonautonomous environment. Moreover, hitherto, most of the published works are devoted to the autonomous NNs , and there are few papers considered nonautonomous NNs [28,29]. For example, in [28,29], the authors considered the following nonautonomous cellular neural networks (CNNs) with time-variable delays and infinite delays…”