Impulsive Stochastic Cohen Grossberg Neural Networks Research Articles

Mean-square stability of delayed stochastic neural networks with impulsive effects driven by [formula omitted]-Brownian motion

This paper studies the mean-square exponential input-to-state stability for a class of delayed impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. By constructing an appropriate G-Lyapunov–Krasovskii functional, mathematical induction approach and some inequality techniques, a new set of sufficient conditions is obtained for the mean-square exponential input-to-state stability of the trivial solutions for the considered systems. Finally, an example is given to illustrate the obtained theory.

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion

ABSTRACTThis paper is devoted to study the stability of a class of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. By means of G-Lyapunov function, Borel–Cantelli lemma and inequality technique, a series of sufficient conditions on pth moment stability and quasi-sure stability with respect to a general decay function are established. A concrete example is given to illustrate the obtained results.

The stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms.

The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated. Under some suitable assumptions and using Lyapunov-Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.

Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, we study an issue of input-to-state stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. The mixed delays consist of varying delays and continuously distributed delays. To the best of our knowledge, the input-to-state stability problem for this class of stochastic system has still not been solved, despite its practical importance. The main aim of this paper is to fill the gap. By constricting several novel Lyapunov–Krasovskii functionals and using some techniques such as the It $$\hat{o}$$ formula, Dynkin formula, impulse theory, stochastic analysis theory, and the mathematical induction, we obtain some new sufficient conditions to ensure that the considered system with/without impulse control is mean-square exponentially input-to-state stable. Moreover, the obtained results are illustrated well with two numerical examples and their simulations.

General decay stability analysis of impulsive neural networks with mixed time delays

To the best of our knowledge, there are only few results on general decay stability applied to stochastic neural networks. In the paper, we study both the pth moment (p≥2) and the almost sure stability on a general decay rate for impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. The presented theory allows us to study the pth moment stability even if the exponential stability cannot be valid. Some examples are given to support and illustrate the theory.

On some stability problems of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

This paper covers the topic of both the pth moment (p⩾2) and almost sure stability of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. We partially use a known result on exponential stability of impulsive stochastic functional differential systems, based on the Razumikhin type technique, and extend it to the case of stochastic neural networks using the Lyapunov function method and a Gronwall type inequality. Additionally, we consider the stability with respect to a general decay function which includes exponential, but also more general lower rate decay functions as the polynomial and the logarithmic ones. This fact gives us the opportunity to study general decay almost sure stability, even when the exponential one cannot be discussed. Suitable examples which support the theory are also presented.

Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks

This paper is concerned with the stability of impulsive stochastic reaction-diffusion differential systems with mixed time delays. First, an equivalent relation between the solution of a stochastic reaction-diffusion differential system with time delays and impulsive effects and that of corresponding system without impulses is established. Then, some stability criteria for the stochastic reaction-diffusion differential system with time delays and impulsive effects are derived. Finally, the stability criteria are applied to impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, and sufficient conditions are obtained for the exponentialp-stability of the zero solution to the neural networks. An example is given to illustrate the effectiveness of our theoretical results. The systems we studied in this paper are more general, and some existing results are improved and extended.

Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays

This paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays and known or unknown parameters. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the mixed time delays under consideration comprise both time-varying delays and continuously distributed delays. To the best of the authors' knowledge, till now, the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper. The main objective of this paper is to fill this gap. By constructing a novel Lyapunov-Krasovskii functional, and using some new approaches and techniques, several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square. The results presented in this paper generalize and improve many known results. Finally, two numerical examples and their simulations are given to show the effectiveness of the theoretical results.

LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, the global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is investigated by using Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) technique. The mixed time delays comprise both the multiple time-varying and continuously distributed delays. Some new sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed model in the stochastic sense using the powerful MATLAB LMI toolbox. The results extend and improve the earlier publications. Two numerical examples are given to illustrate the effectiveness of our results.

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.

Dynamics analysis of impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays

In this paper, the problem of dynamics analysis for a class of new impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on linear matrix inequality (LMI) forms, which can be easily solved by LMI Toolbox in Matlab. An example is given to show the effectiveness of the obtained results.

Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, we study the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. By establishing an L-operator differential inequality with mixed delays and using the properties of M-cone and stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. These results generalize a few previous known results and remove some restrictions on the neural networks. Two examples are also discussed to illustrate the efficiency of the obtained results.

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M -matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p -stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.