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

Fixed-time periodic stabilization of discontinuous reaction–diffusion Cohen–Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction–diffusion Cohen–Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction–diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction–diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

Global Mittag-Leffler synchronization of coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks via sliding mode control.

This paper studies the sliding mode control method for coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks on a directed non-strongly connected topology. A novel fractional integral sliding mode surface and the corresponding control law are designed to realize global Mittag-Leffler synchronization. The sufficient conditions for synchronization and reachability of the sliding mode surface are derived via the hierarchical method and the Lyapunov method. Finally, simulations are provided to verify our theoretical findings.

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.

On the stability of sets for reaction–diffusion Cohen–Grossberg delayed neural networks

In this paper, we introduce the notion of stability of sets for reaction-diffusion Cohen–Grossberg neural networks with time-varying delays. The Lyapunov–Razumikhin technique and a comparison principle are adapted to prove the new stability criteria. In addition, the obtained results are extended to the uncertain case, and the robust stability notion is also investigated. Examples are considered to demonstrate the effectiveness of our results.

Stochastic finite-time stability of reaction-diffusion Cohen–Grossberg neural networks with time-varying delays

This paper investigates the problem of the stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time varying delays using the Dirichlet boundary condition. The concept of finite-time stability for the system is first derived by using the stochastic conditions. By constructing a new Lyapunov–Krasovskii functional and utilizing Jensen’s inequality, Wirtinger’s type inequality technique, the Gronwall inequality and the linear matrix inequality (LMI) frame work, conditions are obtained which guarantee the stochastically finite-time stability of Cohen–Grossberg neural networks. Finally, two numerical examples are given to show the effectiveness of the proposed results.

Passivity and Synchronization of Coupled Reaction–Diffusion Cohen–Grossberg Neural Networks with Fixed and Switching Topologies

This paper investigates the passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs) with constant and delayed couplings respectively. On the one side, a CRDCGNNs model with fixed topology is introduced, and several sufficient conditions which ensure passivity and synchronization for this type of network are derived respectively by exploiting some inequality techniques and constructing appropriate Lyapunov functional. On the other side, considering that topology structure of a network may change by switches in some cases, we also concern on the passivity and synchronization of CRDCGNNs with switching topology. Finally, the correctness of the obtained passivity and synchronization criteria are corroborated by two illustrative examples.

Passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks with state coupling and spatial diffusion coupling

This paper deals with the passivity and synchronization problems for two types of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs). On the one side, a CRDCGNNs model with state coupling is introduced, and several sufficient conditions which ensure the passivity and synchronization of this type of network are deduced respectively by resorting to some inequality techniques and Lyapunov functional method. On the other side, considering that the different diffusion of each node may give rise to different changes of other nodes in reaction–diffusion networks, we also carry out some investigations on the passivity and synchronization of CRDCGNNs with spatial diffusion coupling. Finally, the correctness of the obtained research results are corroborated by two illustrative examples.

Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms

This paper is devoted to the global exponential and fixed-time synchronization of delayed reaction-diffusion Cohen–Grossberg neural networks. Adaptive controllers are designed such that the addressed system can realize global exponential synchronization goal under the framework of inequality techniques, Lyapunov method as well as some suitable assumptions. Furthermore, as corollaries, the corresponding conclusion is provided to ensure the delayed Cohen–Grossberg neural networks without reaction-diffusion term can reach fixed-time synchronization goal. In addition, the settling time of fixed-time synchronization can be adjusted to desired values regardless of initial conditions, which is more reasonable. Finally, two numerical examples and its simulations are given to show the effectiveness of the obtained 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.

Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincarè inequality

In this paper, we formulate and investigate the passivity analysis of delayed reaction-diffusion neural networks with Cohen-Grossberg type. The derivative of the Lyapunov-Krasovskii functional was estimated by the new agencies of Hardy-Poincarè inequality and some analysis techniques. Subsequently, some new and concise conditions to check the passivity of the given Cohen-Grossberg neural networks were summarized. The proposed criteria not only depends on the system parameters, reaction-diffusion coefficients but also on the regional feature. Furthermore, as corollaries, some sufficient schemes are provided to achieve passive and exponential passive of delayed Cohen-Grossberg neural networks without reaction-diffusion term. The results obtained in this paper generalize and improve many known results. Finally, two numerical examples and its simulations are proposed to show the effectiveness and merits of the improved 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.

$${\varvec{p}}$$ p th Moment Exponential Stability of Hybrid Delayed Reaction–Diffusion Cohen–Grossberg Neural Networks

In this paper, we propose hybrid reaction–diffusion Cohen–Grossberg neural networks (RDCGNNs) with variable coefficients and mixed time delays. By using the Lyapunov–Krasovkii functional approach, stochastic analysis technique and Hardy inequality, some novel sufficient conditions are derived to ensure the pth moment exponential stability of hybrid RDCGNNs with mixed time delays. The obtained sufficient conditions are relevant to the diffusion terms. The results of this paper are novel and improve some of the previously known results. Finally, two numerical examples are provided to verify the usefulness of the obtained 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.

Delay-dependent LMI-based robust stability criterion for discrete and distributed time-delays Markovian jumping reaction–diffusion CGNNs under Neumann boundary value

In this paper, variational methods, Lyapunov stability theory, Homomorphic mapping theory, M-matrix, H-matrix and linear matrix equality (LMI) technique are synthetically employed to obtain the LMI-based stochastically exponential robust stability criterion for a discrete and distributed time-delays Markovian jumping reaction–diffusion Cohen–Grossberg neural networks (CGNNs) with uncertain parameters. It is worth mentioning that the methods employed in this paper improve those of previous related literature to some extent, and the obtained stability criterion can be easily and efficiently computed by computer LMI toolbox. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods thanks to the large allowable variation range of time-delays.

Stability analysis of Markovian jumping impulsive stochastic delayed RDCGNNs with partially known transition probabilities

This paper considers the robust stability for a class of Markovian jump impulsive stochastic delayed reaction-diffusion Cohen-Grossberg neural networks with partially known transition probabilities. Based on the Lyapunov stability theory and linear matrix inequality (LMI) techniques, some robust stability conditions guaranteeing the global robust stability of the equilibrium point in the mean square sense are derived. To reduce the conservatism of the stability conditions, improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. An example shows the proposed theoretical result is feasible and effective.

Delay-Dependent exponential stability for nonlinear reaction-diffusion uncertain Cohen-Grossberg neural networks with partially known transition rates via Hardy-Poincaré inequality

In this paper, stochastic global exponential stability criteria for delayed impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks (CGNNs for short) are obtained by using a novel Lyapunov-Krasovskii functional approach, linear matrix inequalities (LMIs for short) technique, Ito formula, Poincare inequality and Hardy-Poincare inequality, where the CGNNs involve uncertain parameters, partially unknown Markovian transition rates, and even nonlinear p-Laplace diffusion (p > 1). It is worth mentioning that ellipsoid domains in ℝ m (m ≥ 3) can be considered in numerical simulations for the first time owing to the synthetic applications of Poincare inequality and Hardy-Poincare inequality. Moreover, the simulation numerical results show that even the corollaries of the obtained results are more feasible and effective than the main results of some recent related literatures in view of significant improvement in the allowable upper bounds of delays.

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.