Stabilization of delayed Cohen‐Grossberg BAM neural networks

This paper deals with finite‐time stabilization results of delayed Cohen‐Grossberg BAM neural networks under suitable control schemes. We propose a state‐feedback controller together with an adaptive‐feedback controller to stabilize the system of delayed Cohen‐Grossberg BAM neural networks. Stabilization conditions are derived by using Lyapunov function and some algebraic conditions. We also estimate the upper bound of settling time functional for the stabilization, which depends on the controller schemes and system parameters. Two illustrative examples and numerical simulations are given to validate the success of the derived theoretical results.     

Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects

In this paper, we consider a class of delayed quaternion‐valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti‐periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti‐periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real‐valued or complex‐valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results.     

Stability criteria for stochastic Takagi‐Sugeno fuzzy Cohen‐Grossberg BAM neural networks with mixed time‐varying delays

This article is concerned with the asymptotic stability analysis of Takagi–Sugeno stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed time‐varying delays. Based on the Lyapunov functional and linear matrix inequality (LMI) technique, sufficient conditions are derived to ensure the global convergence of the equilibrium point. The proposed conditions can be checked easily by LMI Control Toolbox in Matlab. It has been shown that the results are less restrictive than previously known criteria. They are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. Numerical examples are given to demonstrate the effectiveness of our results. © 2014 Wiley Periodicals, Inc. Complexity 21: 143–154, 2016     

Stability analysis of Takagi–Sugeno fuzzy Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays

In this paper, the global asymptotic stability problem of Takagi–Sugeno (TS) fuzzy Cohen–Grossberg Bidirectional Associative Memory neural networks (FCGBAMNNs) with discrete and distributed time-varying delays is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of FCGBAMNNs which are represented by TS fuzzy models. Our results can be easily verified and are also less restrictive than previously known criteria and can be applied to Cohen–Grossberg neural networks, recurrent neural networks and cellular neural networks. Finally, the proposed stability conditions are demonstrated with a numerical example.     

Global exponential stability analysis of Cohen–Grossberg neural network with delays

This brief presents new sufficient conditions of globally exponential stability of Cohen–Grossberg neural networks with time delays. The results are also compared with previously reported results in the literature, implying that the results obtained in this paper provide one more set of criteria for determining the global exponential stability of Cohen–Grossberg neural networks with time delays.     

Convergence analysis for second-order interval Cohen–Grossberg neural networks

This paper presents new theoretical results on global stability of a class of second-order interval Cohen–Grossberg neural networks. The new criteria is derived to ensure the existence, uniqueness and global stability of the equilibrium point of neural networks under uncertainties. And we make some comparisons between our results with the existed corresponding results. Some examples are provided to show the effectiveness of the obtained results.     

Global exponential stability of impulsive Cohen–Grossberg neural network with time-varying delays

In this paper, the impulsive Cohen–Grossberg neural network model with time-varying delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural network with time-varying delays. These results generalize a few previous known results and remove some restrictions on the neural network. An example is given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural network.     

Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

In this paper, a class of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion is formulated and investigated. By employing delay differential inequality and the linear matrix inequality (LMI) optimization approach, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg neural networks. An example is given to show the effectiveness of the results obtained here.     

Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays

In this paper, the Cohen–Grossberg neural network model with both time-varying and continuously distributed delays is considered. Without assuming both global Lipschitz conditions on these activation functions and the differentiability on these time-varying delays, applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of equilibrium point for Cohen–Grossberg neural network with both time-varying and continuously distributed delays. These results generalize and improve the earlier publications. Two numerical examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural networks.     

Dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays

This paper studies the Cohen–Grossberg neural networks with variable and time-varying delays. By applying Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the uniform boundedness, point dissipativeness and global exponential stability for general Cohen–Grossberg neural networks. And then, some sufficient conditions on the existence and global exponential stability of periodic solutions for periodic Cohen–Grossberg neural networks are established, either. Those results obtained in this paper extend and generalize the corresponding results existing in previous literature. These criteria are important in signal processing and the design of networks.     

New sufficient conditions for global asymptotic stability of Cohen–Grossberg neural networks with time-varying delays

In this paper, a class of Cohen–Grossberg neural networks with time-varying delays are considered. Without assuming the boundedness and monotonicity of activation functions, we establish new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for such delayed Cohen–Grossberg neural networks. Numerical examples are provided to show that the proposed criteria are less conservative than some results in the literature.     

Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

In this paper, based on the topological degree theory, Lyapunov functional method and inequality analysis technique, the existence and global exponential stability of equilibrium of impulsive fuzzy Cohen–Grossberg bi‐directional associative memory neural networks with delays, are investigated. Moreover, an illustrative example is given to demonstrate the effectiveness of the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Global attractivity in delayed Cohen–Grossberg neural network models

In this paper, we investigate the global attractivity of Cohen–Grossberg neural network models with connection time delays for both discrete and distributed cases via the Lyapunov functional method. Without assuming the monotonicity and differentiability of activation functions and the symmetry of connection matrix, we establish three new sufficient conditions for the global exponential stability of a unique equilibrium for the delayed Cohen–Grossberg neural network no matter whether the connection time delay is of discrete type or distributed type. In particular, all the three new criteria are independent of time delays and do not include one another. To demonstrate the differences and features of the new stability criteria, several examples are discussed to compare the present results with the existing ones.     

Existence and stability of almost periodic solution for Cohen–Grossberg neural networks with variable coefficients

This paper is devoted to the existence and globally exponential stability of almost periodic solution for a class of Cohen–Grossberg neural networks with variable coefficients. By using Banach fixed point theorem and applying inequality technique, we give some sufficient conditions ensuring the existence and globally exponential stability of almost periodic solution. These results have important leading significance in designs and applications of Cohen–Grossberg neural networks. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis.     

On periodic solutions to a class of non-autonomously delayed reaction-diffusion neural networks

In this paper, we investigate the existence and attractivity of periodic solutions for non-autonomous reaction-diffusion Cohen–Grossberg neural networks with discrete time delays. By combining the Lyapunov functional method with the contraction mapping principle and Poincaré inequality, we establish several criteria for the existence and global exponential stability of periodic solutions. More interestingly, Poincaré inequality is used to handle the reaction-diffusion terms, hence all the criteria depend on reaction-diffusion terms. These criteria are applicable in Cohen–Grossberg neural networks with both the Dirichlet and the Neumann boundary conditions on a general space domain. Several examples with numerical simulations are given to demonstrate the results.     

Exponential stability of Cohen–Grossberg neural networks with delays

The exponential stability characteristics of the Cohen–Grossberg neural networks with discrete delays are studied in this paper, without assuming the symmetry of connection matrix as well as the monotonicity and differentiability of the activation functions and the self-signal functions. By constructing suitable Lyapunov functionals, the delay-independent sufficient conditions for the networks converge exponentially towards the equilibrium associated with the constant input are obtained. By employing Halanay-type inequalities, some sufficient conditions for the networks to be globally exponentially stable are also derived. It is not doubt that our results are significant and useful for the design and applications of the Cohen–Grossberg neural networks.     

Some criteria for robust stability of Cohen–Grossberg neural networks with delays

This paper considers the problem of robust stability of Cohen–Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen–Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results.     

Global robust stability criteria of stochastic Cohen–Grossberg neural networks with discrete and distributed time-varying delays

The paper is concerned with the problem of robust asymptotic stability analysis of stochastic Cohen–Grossberg neural networks with discrete and distributed time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technology, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed conditions can be checked easily by LMI Control Toolbox in Matlab. Furthermore, all the results are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. A numerical example is given to demonstrate the effectiveness of our results.     

Global stability for discrete Cohen–Grossberg neural networks with finite and infinite delays

In this paper, the global stability problem for a general discrete Cohen–Grossberg neural network with finite and infinite delays is investigated. A simple criterion ensuring the global asymptotical stability is established, by applying the Lyapunov method and graph theory. Finally, an example showing the effectiveness of the provided criterion is given.