Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks

Abstract

In this paper, without transforming the original inertial neural networks into the first-order differential equation by some variable substitutions, time-varying delays are introduced into inertial Cohen-Grossberg-type networks and the existence, the uniqueness, and the asymptotic stability and synchronisation for the neural networks are investigated. Firstly, the existence of a unique equilibrium point is proved by using nonlinear Lipschitz measure method. Second, by finding a new Lyapunov-Krasovskii functional, some sufficient conditions are derived to ensure the asymptotic stability, the asymptotic synchronization, and the asymptotic adaptive synchronization. The results of this paper are new and they complete previously known results. We illustrate the effectiveness of the approach through a few examples.

Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

“…Since 1983 Cohen-Grossberg neural networks are ones of the most investigated neural network models, and numerous qualitative results have been reported in the literature [2]- [6]. The emergence of new results on Cohen-Grossberg type of neural networks demonstrates the importance of research on their dynamic analysis for mathematical, computational, neurophysiological and engineering theories, as well as of their real applications [7], [8].…”

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

“…That is why numerous researchers considered delay effects on both Cohen-Grossberg and BAM neural networks, and excellent results have been reported in the literature. We will direct the reader to see [9][10][11] for some results on delayed Cohen-Grossberg neural networks, and [8,[12][13][14] for results on BAM neural networks with delays, including some very recent publications [15][16][17][18].…”

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

“…It is also well known that some powerful from the applied point of view neural network models, such as cellular neural networks, bidirectional neural networks, Hopfield neural networks, can be considered as special cases of CGNNs. Later on, the investigations on delayed CGNNs with constants and time-varying delays also had increased rapidly [5][6][7] including some recent results [8][9][10]. In addition, the subject of reaction-diffusion delayed CGNNs has been studied in [11][12][13][14].…”

“…Asymptotic stability of equilibrium states is one of the most important qualitative properties that has to be guaranteed in most of the applications of neural network models designed. This is why most of the existing results on neural network systems are related to asymptotic or exponential stability of equilibrium states [2][3][4][8][9][10]12,16,17,[22][23][24]30,33,35,37,45].…”