Stochastic Reaction-diffusion Cohen-Grossberg Neural Networks Research Articles

Event-Triggered Controller on Practically Exponential Input-to-State Stabilization of Stochastic Reaction–Diffusion Cohen–Grossberg Neural Networks and Its Application to Image Encryption

Event-Triggered Controller on Practically Exponential Input-to-State Stabilization of Stochastic Reaction–Diffusion Cohen–Grossberg Neural Networks and Its Application to Image Encryption

Intermittent boundary stabilization of stochastic reaction–diffusion Cohen–Grossberg neural networks

Cohen–Grossberg neural networks (CGNNs) play an important role in many applications and the stabilization of this system has been well studied. This study considers the exponential stabilization for stochastic reaction–diffusion Cohen–Grossberg neural networks (SRDCGNNs) by means of an aperiodically intermittent boundary control. Both SRDCGNNs without and with time-delays are discussed. By employing the spatial integral functional method and Poincare’s inequality, criteria are derived to ensure the controlled systems achieve mean square exponential stabilization. Based on these criteria, the effects of diffusion item, control gains, the minimum control proportion and time-delays on exponential stability are analyzed. Examples are given to illustrate the effectiveness of the obtained theoretical results.

Synchronization analysis for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions via periodically intermittent control

In this paper, mathematical analysis is proposed on the synchronization problem for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions. By introducing several important inequalities and using Lyapunov functional technique, some new synchronization criteria in terms of p-norm are derived under periodically intermittent control. Some previous known results in the literature are improved, and some restrictions on the mixed time-varying delays are removed. The influence of diffusion coefficients, diffusion space, stochastic perturbation and control width on synchronization is analyzed by the obtained synchronization criteria. Numerical simulations are presented to show the feasibility of the theoretical results.

Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and Wiener processes

In this paper, we study delayed reaction–diffusion Cohen–Grossberg neural networks driven by infinite dimensional Wiener processes. Based on semigroup theory, existence and uniqueness of mild solutions are proved under global Lipschitz conditions. Then, some criteria of global exponential stability are obtained by using Lyapunov method and Halanay inequality. Finally, some interesting examples are provided to show the feasibility and usefulness of the developed results.

Graph-theoretic approach to exponential synchronization of stochastic reaction–diffusion Cohen–Grossberg neural networks with time-varying delays

A stochastic reaction–diffusion Cohen–Grossberg neural network (CGNN) with time-varying delays is concerned. In the model, time delay effects, diffusion effects and the white noise are taken into account at the same time. Based on graph theory and Lyapunov method, the sufficient conditions for exponential synchronization are considered. This method is different from the traditional methods. Two different types of sufficient criteria for synchronization are presented in the form of Lyapunov functions and the coefficients of drive-response network9s, respectively. They both reveal the relationship between exponential synchronization and the topology structure of the systems. Finally, several numerical simulation figures are illustrated to show the effectiveness of the obtained results.

Asymptotic stability analysis of stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed time delays

In this paper, the asymptotic stability problem is studied for a class of stochastic Cohen–Grossberg neural networks with reaction–diffusion and time-mixed delays. By using the Lyapunov–Krasovskii functional, stochastic analysis technology and linear matrix inequalities (LMIs) technique, several sufficient conditions on the asymptotic stability for the considered system are obtained. The condition not only connects with the delays and diffusion effect, but also relates to the magnitude of noise. Therefore, these stability criteria are essentially new and more effective than those given in previous conditions. Two examples are presented to illustrate the effectiveness and efficiency of the results.

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.

Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincare inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.

Exponential stability analysis of stochastic reaction-diffusion Cohen–Grossberg neural networks with mixed delays

In this paper, we study a new class of stochastic Cohen–Grossberg neural networks with reaction-diffusion and mixed delays. Without the aid of nonnegative semimartingale convergence theorem, the method of variation parameter and linear matrix inequalities technique, a set of novel sufficient conditions on the exponential stability for the considered system is obtained by utilizing a new Lyapunov–Krasovskii functional, the Poincaré inequality and stochastic analysis theory. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Therefore, our results generalize and improve some earlier publications. Moreover, two numerical examples are given to show the effectiveness of the theoretical results and demonstrate that the stability criteria existed in the earlier literature fail.

Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays

This paper is concerned withpth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions onpth moment exponential stability for the considered system is presented. The proposed results generalized and improved some earlier publications.

Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincare inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions, which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results.

Exponential stability of stochastic reaction–diffusion Cohen–Grossberg neural networks with delays

In this paper, stochastic Cohen–Grossberg neural network with time-varying delays and reaction–diffusion terms is considered. The sufficient conditions are obtained to guarantee the mean value exponential stability of an equilibrium solution.