Global attracting sets for neutral-type BAM neural networks with time-varying and infinite distributed delays

In this paper, the asymptotic property of a class of neutral-type BAM neural networks with time-varying and infinite distributed delays is discussed. By developing a new integral inequality and applying the properties of nonnegative matrix, some sufficient conditions for the Lagrange stability and the existence of the global attracting set of the considering model are obtained. Meanwhile, the estimation of the global attractive set is also given out. The results derived here generalize and improve the earlier publications. Finally, two numerical examples are given and analyzed to demonstrate our results.     

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.     

Global exponential stability for BAM neural networks with time-varying delays in the leakage terms

In this paper, we first investigate the existence of a unique equilibrium to general bidirectional associative memory neural networks with time-varying delays in the leakage terms by the fixed point theorem. Then, by constructing a Lyapunov functional, we establish some sufficient conditions on the global exponential stability of the equilibrium for such neural networks, which substantially extend and improve the main results of Gopalsamy [K. Gopalsamy, Leakage delays in BAM, J. Math. Anal. Appl. 325 (2007) 1117–1132].     

Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations

In this paper, the problems of global dissipativity are investigated for neural networks with mixed time-varying delays and discontinuous activations. Some new criteria for checking the global dissipativity of the addressed neural networks are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and M-matrix properties. Finally, two numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.     

Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays

In the current paper, BAM neural networks with time-varying coefficients and distributed time delays are studied. Sufficient conditions guaranteeing the exponential componentwise convergence and existence of one unique periodic solution are obtained by the comparison principle, continuation theorem of topological degree and inequality techniques. The boundedness and differentiability of activation functions are removed. The obtained sufficient criteria are easy to verify and are hence very useful in applications.     

Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays

This paper is concerned with the problem of passivity analysis for a class of Cohen-Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen-Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with reaction-diffusion and mixed delays. The mixed delays considered in this paper are time-varying and distributed delays. Based on a new Lyapunov-Krasovskii functional and the Poincaré inequality as well as stochastic analysis theory, a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Moreover, two numerical examples are given to show the effectiveness of the theoretical results.     

Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic jumping bidirectional associative memory (BAM) neural networks with time-varying and distributed delays. To the best of our knowledge, this class of stochastic jumping BAM neural networks with time-varying and distributed delays has never been investigated in the literature. The main aim of this paper tries to fill the gap. By using the stochastic stability theory, the properties of a Brownian motion, the generalized Ito’s formula and linear matrix inequalities technique, some novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. In particular, the activation functions considered in this paper are fairly general since they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, the derivative of time delays is not necessarily zero or small than 1. In summary, the results obtained in this paper extend and improve those not only with/without noise disturbances, but also with/without Markovian jump parameters. Finally, two interesting examples are provided to illustrate the theoretical results.     

Global exponential stability of fuzzy BAM neural networks with transmission delays

In this paper, a class of fuzzy bidirectional associated memory (BAM) neural networks with transmission delays are studied. Some sufficient conditions are established for the existence , uniqueness and global exponential stability of equilibrium point. The sufficient conditions are easy to verify at pattern recognition and automatic control. Finally, an example is given to show feasibility and effectiveness of our results.     

Global exponential stability of BAM neural networks with distributed delays and impulses

Convergence dynamics of bi-directional associative memory (BAM) neural networks with continuously distributed delays and impulses are discussed. Without assuming the differentiability and the monotonicity of the activation functions and symmetry of synaptic interconnection weights, sufficient conditions to guarantee the existence and global exponential stability of a unique equilibrium are given.     

Global asymptotic stability of BAM neural networks with mixed delays and impulses

In this paper, BAM neural networks with mixed delays and impulses are considered. A new set of sufficient conditions are derived by constructing suitable Lyapunov functional with matrix theory for the global asymptotic stability of BAM neural networks with mixed delays and impulses. Moreover, an example is also provided to illustrate the effectiveness of the results.     

New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays

In this paper, we consider the problem of passivity analysis issue for a class of stochastic fuzzy BAM neural networks with time varying delays. By employing the idea of delay-fractioning technique and Lyapunov stability theory, a new set of sufficient conditions are derived in terms of linear matrix inequalities for obtaining the passivity condition of the considered neural network model. First, we derive the passivity condition for stochastic fuzzy BAM neural networks with time varying delays and then the result is extended to the case with uncertainties. Two numerical examples are given to illustrate the effectiveness and conservatism of the obtained results.     

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.     

Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.     

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.     

Global robust stability of interval cellular neural networks with time-varying delays

This paper studies the global robust asymptotic stability (GRAS) and global robust exponential stability (GRES) of delayed cellular neural networks with time-varying delays. A series of new criteria concerning GRAS and GRES are obtained by employing the Young's inequality, Halanay's inequality and Lyapunov functional and combine with some analysis techniques. Several previous results are improved and generalized. Some examples and remarks are also given to illustrate the effectiveness of the results. In addition, these criteria possess important leading significance in design and applications of global stable DCNNs, and are of great interest in many applications.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays

In this paper, the global robust exponential stability for a class of delayed BAM neural networks with norm-bounded uncertainty is studied. Some less conservative conditions are presented for the global exponential stability of BAM neural networks with time-varying delays by constructing a new class of Lyapunov functionals combined with free-weighting matrices. This novel approach, based on the linear matrix inequality (LMI) technique, removes some existing restrictions on the system’s parameters, and the derived conditions are easy to verify via the LMI toolbox. Comparisons between our results and previous results admit that our results establish a new set of stability criteria for delayed BAM neural networks.     

Global exponential stability of a class of neural networks with delays

This paper is concerned with the stability of neural networks with time-varying delays. Under assumption that the nonlinear stimulate functions are Lipschitz continuous, by means of generalized Halanay inequalities, Dini＇s derivative and functional analysis techniques, several globally exponential stability criteria are established, which are only dependent on the parameters of the system.     

Dynamics of a class of Cohen–Grossberg neural networks with time-varying delays

Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, we establish some sufficient conditions for the global exponential stability of a unique equilibrium and the existence of periodic solution for the Cohen–Grossberg neural network with time-varying delays. Brouwer's fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis are employed. Our results are all independent of the delays and maybe more convenient to design a circuit network.