Associative Memory Neural Networks Research Articles

Non-fragile synchronization of memristive BAM networks with random feedback gain fluctuations

This paper investigates the non-fragile synchronization for bidirectional associative memory (BAM) neural networks with time-varying delays. A memristor-based BAM neural network is formulated and sufficient conditions are derived to guarantee its synchronization based on master–slave system approach. The non-fragile observer based feedback controller gains are assumed to have the random fluctuations, two different types of uncertainties which perturb the gains are taken into account. The Lyapunov–Krasovskii stability theory together with linear matrix inequality (LMI) approach is used to derive the delay-dependent criteria to ensure the asymptotic stability of the error system, which guarantees the master system synchronize with the slave system. The expressions for the non-fragile controller can be obtained by solving a set of LMIs using standard MATLAB toolboxes. Finally, numerical example on the chaotic system is presented to illustrate the effectiveness of the theoretical results.

Stability of bidirectional associative memory neural networks with Markov switching via ergodic method and the law of large numbers

This paper devotes to stability analysis of continuous time and discrete time bidirectional associative memory (BAM) neural networks whose parameters are randomly varying in a finite state Markov chain sense. Based on the ergodic theory of continuous time Markov chain, the matrix measure approach and Lyapunov theory, almost sure stability and exponential stability in the mean square for continuous time BAM neural networks are derived. We also present some new stability results for discrete time BAM neural networks with the help of the law of large numbers. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in stability of neural networks.

Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities

In this paper, we formulate and investigate the impulsive synchronization of memristor based bidirectional associative memory (BAM) neural networks with time varying delays. Based on the linear matrix inequality (LMI) approach, the impulsive time dependent results are derived for the exponential stability of the error system, which guarantees the exponential synchronization of the BAM model by means of master–slave synchronization concept. Different from the existing models, an observer (slave system) for the considered BAM neural network in this paper is modeled with time-varying and random impulse moments. Some sufficient conditions are obtained to guarantee the exponential synchronization of the BAM model is derived by using the time-varying Lyapunov function. Simple LMI expressions are proposed to find the feedback controller gains at impulse instants. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

The stabilization of BAM neural networks with time-varying delays in the leakage terms via sampled-data control

This paper is concerned with the stabilization of bidirectional associative memory neural networks with time-varying delays in the leakage terms using sampled-data control. We apply an input delay approach to change the sampling system into a continuous time-delay system. Based on the Lyapunov theory, some stability criteria are obtained. These conditions are expressed in terms of linear matrix inequalities and can be solved via standard numerical software. Finally, one numerical example is given to demonstrate the effectiveness of the proposed results .

Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters

This paper addresses the mean square exponential stabilization problem of stochastic bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time-varying delays. By establishing a proper Lyapunov–Krasovskii functional and combining with LMIs technique, several sufficient conditions are derived for ensuring exponential stabilization in the mean square sense of such stochastic BAM neural networks. In addition, the achieved results are not difficult to verify for determining the mean square exponential stabilization of delayed BAM neural networks with Markovian jumping parameters and impose less restrictive and less conservative than the ones in previous papers. Finally, numerical results are given to show the effectiveness and applicability of the achieved results.

Global exponential stability and periodic solutions of high-order bidirectional associative memory (BAM) neural networks with time delays and impulses

High-order bidirectional associative memory (BAM) neural networks with mixed features such as time delays and impulses play an increasingly important role in the design and implementation of neural network systems. It exhibits advantage of stronger approximation property, faster convergence rate, greater storage capacity and higher fault tolerance than low-order neural networks. In this paper, issues of both stability and periodicity for a class of high-order BAM neural networks with time delays and impulses are investigated. With M-matrix theory, linear matrix inequality technique, fixed point theorem and Lyapunov approach, we derive new sufficient conditions for achieving global exponential stability of equilibrium point and the existence and global exponential stability of periodic solutions for the addressed high-order BAM neural networks. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Existence, uniqueness and global exponential stability of a periodic solution for a class of multidirectional associative memory neural network models

A multidirectional associative memory (MAM) neural network with periodic coefficients and distributed delays is studied. By constructing a Poincare mapping, some sufficient conditions are obtained ensuring existence, uniqueness and the global exponential stability of a periodic solution of MAM neural network. The result is new to MAM neural networks. An example is given to illustrate the effectiveness of the result.

Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays

Among the various fuzzy models, the well-known Takagi–Sugeno (T–S) fuzzy model is recognized as a popular and powerful tool in approximating a complex nonlinear system. T–S model provides a fixed structure to some nonlinear systems and facilitates the analysis of the system. This paper deals with the global stability of stochastic bidirectional associative memory (BAM) neural networks with discrete and distributed time-varying delays which are represented by the T–S fuzzy models. The stability conditions are derived using Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) techniques. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.

Design of state estimator for bidirectional associative memory neural networks with leakage delays

This paper considers the issue of state estimation for a class of bidirectional associative memory (BAM) neural networks. More precisely, the BAM model is considered with mixed delays which includes a constant delay in the leakage term, time-varying discrete delay and constant distributed delay. By constructing a novel Lyapunov–Krasovskii functional (LKF) together with free-weighting matrix technique, a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that, for all admissible delay bounds, the resulting estimation error system is globally asymptotically stable. Also it is assumed that the derivative of time delay is not necessarily zero or less than one. Further the derived conditions are formulated in terms of a set of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory. The result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored.

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.

Global robust asymptotic stability of variable-time impulsive BAM neural networks

In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B-equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010), Akhmet and Perestyuk (1990) and Akhmet and Turan (2009), we reduce these networks to a fix time impulsive neural networks system. Sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, we give one illustrative example to show the effectiveness of the theoretical results.

Further results on robust stability of bidirectional associative memory neural networks with norm-bounded uncertainties

Abstract In this paper, we have a further study about global robust stability of dynamical bidirectional associative memory (BAM) neural networks with norm-bounded uncertainties. By introducing four new upper bound norms for the interconnection matrices of the neural networks and constructing a suitable Lyapunov functional, several new criteria on global robust stability are established. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. In comparison with the results reported in the literature, the proposed approach leads to results with less restrictive conditions. Two numerical examples are also worked through to illustrate our results.

Almost periodic solution for multidirectional associative memory neural network with distributed delays

This paper proposes a mathematical model of multidirectional associative memory (MAM) neural network with almost periodic coefficients and continuously distributed delays. By using exponential dichotomy and spectral radius, a sufficient condition for the existence and the global exponential stability of an almost periodic solution is obtained. Two examples are given to illustrate the effectiveness of our results.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

Anti-periodic solutions in a ring of four neurons with multiple delays

This paper is concerned with the existence and exponential stability of anti-periodic solutions of bidirectional associative memory (BAM) neural networks with multiple delays. Applying inequality techniques and Lyapunov method, Sufficient conditions which ensure the existence and exponential stability of anti-periodic solutions of the BAM neural networks are presented. Our results are new and supplement some previously known ones.

Memristor-based chaotic neural networks for associative memory

In chaotic neural networks, the rich dynamic behaviors are generated from the contributions of spatio-temporal summation, continuous output function, and refractoriness. However, a large number of spatio-temporal summations in turn make the physical implementation of a chaotic neural network impractical. This paper proposes and investigates a memristor-based chaotic neural network model, which adequately utilizes the memristor with unique memory ability to realize the spatio-temporal summations in a simple way. Furthermore, the associative memory capabilities of the proposed memristor-based chaotic neural network have been demonstrated by conventional methods, including separation of superimposed pattern, many-to-many associations, and successive learning. Thanks to the nanometer scale size and automatic memory ability of the memristors, the proposed scheme is expected to greatly simplify the structure of chaotic neural network and promote the hardware implementation of chaotic neural networks.

Multistability and Multiperiodicity for a Class of Cohen–Grossberg BAM Neural Networks with Discontinuous Activation Functions and Time Delays

In this paper, a general class of Cohen---Grossberg bidirectional associative memory neural networks (CGBAMNNs) with time-varying delays, distributed delays and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and local exponential stability of multiple equilibrium points, which ensure that $$2n$$2n-dimensional CGBAMNNs with $$k$$k-level discontinuous activation functions can have $$k^n$$kn equilibrium points. As an extension of multistability, sufficient conditions are obtained to ensure the existence of $$k^n$$kn locally exponentially stable periodic orbits of the system when time-varying delays and external inputs are periodic. Finally, three examples are given to illustrate the feasibility and application of the obtained results.

Novel LMI-Based Condition on Global Asymptotic Stability for a Class of Cohen–Grossberg BAM Networks With Extended Activation Functions

This paper is concerned with global asymptotic stability of a class of Cohen-Grossberg bidirectional associative memory (BAM) neural networks with delays. Under the assumptions that the activation functions only satisfy the so-called extended global Lipschitz condition and the behaved functions only satisfy global Lipschitz condition, we apply linear matrix inequality (LMI) method and homeomorphism theory to propose a new LMI-based sufficient condition for global asymptotic stability of the concerned neural networks. In our results, the extended global Lipschitz condition on the activation functions is less conservative than the assumptions for boundedness and monotonicity and is weaker than the assumption for the general global Lipschitz condition, the global Lipschitz condition on the behaved functions is also less conservative than the assumptions for monotonicity and differentiability in existing papers.

Improved robust stability criteria for bidirectional associative memory neural networks under parameter uncertainties

This paper deals with the global robust stability problem of dynamical bidirectional associative memory neural networks with multiple time delays under parameter uncertainties. Using some new upper bound norms for the interconnection matrices of the neural networks and constructing suitable Lyapunov functional, we derive novel conditions for the global robust asymptotic stability of equilibrium point. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. It is shown that the established stability condition generalizes some existing ones, and it can be considered to an alternative result to some other corresponding results derived in previous literature. We also provide two comparative numerical examples to illustrate the advantages of our result over the previously published corresponding robust stability results.

Global Exponential Synchronization of Delayed BAM Neural Networks

In order to enhance the presented synchronization scheme level, this paper deals with the synchronization problem of a class of bidirectional associative memory (BAM) neural networks with delays. Using the drive-response concept, a feedback control law is derived to achieve the state synchronization of two identical BAM neural networks. Moreover, based on the Lyapunov stability method and the Halanay inequality lemma, two delay-independent sufficient exponential synchronization conditions are derived. The results in the present study provide new insights into the exponential synchronization of BAM neural networks. An example is given to show the effectiveness of the obtained results