Bidirectional Associative Memory Networks Research Articles

Bifurcation analysis in a discrete BAM network model with delays

In this paper, a discrete bidirectional associative memory network model consisting of three neurons is considered. We study the stability of the equilibria of the system by analysing the distribution of the eigenvalues. It is found that there are three kinds of bifurcations: Pitchfork bifurcation, Period-Doubling bifurcation and Neimark–Sacker bifurcation. The direction and stability of the Neimark–Sacker are determined by using normal forms and centre manifold theory. Some numerical simulations are carried out to illustrate the analytical results.

Exponential ${\rm H}_{\infty}$ Synchronization of General Discrete-Time Chaotic Neural Networks With or Without Time Delays

This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.

Bi-periodicity evoked by periodic external inputs in delayed Cohen–Grossberg-type bidirectional associative memory networks

In this paper, the bi-periodicity issue is discussed for Cohen–Grossberg–type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with time-varying delays and standard activation functions. It is shown that the model considered in this paper has two periodic orbits located in saturation regions and they are locally exponentially stable. Meanwhile, some conditions are derived to ensure that, in any designated region, the model has a locally exponentially stable or globally exponentially attractive periodic orbit located in it. As a special case of bi-periodicity, some results are also presented for the system with constant external inputs. Finally, four examples are given to illustrate the effectiveness of the obtained results.

Computation of Synchronized Periodic Solution in a BAM Network With Two Delays

A bidirectional associative memory (BAM) neural network with four neurons and two discrete delays is considered to represent an analytical method, namely, perturbation-incremental scheme (PIS). The expressions for the periodic solutions derived from Hopf bifurcation are given by using the PIS. The result shows that the PIS has higher accuracy than the center manifold reduction (CMR) with normal form for the values of time delay not far away from the Hopf bifurcation point. In terms of the PIS, the necessary and sufficient conditions of synchronized periodic solution arising from a Hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form. It can be seen that theoretical analysis is in good agreement with numerical simulation. It implies that the provided method is valid and the obtained result is correct. To the best of our knowledge, the paper is the first one to introduce the PIS to study the periodic solution derived from Hopf bifurcation for a 4-D delayed system quantitatively.

BAM Learning of Nonlinearly Separable Tasks by Using an Asymmetrical Output Function and Reinforcement Learning

Most bidirectional associative memory (BAM) networks use a symmetrical output function for dual fixed-point behavior. In this paper, we show that by introducing an asymmetry parameter into a recently introduced chaotic BAM output function, prior knowledge can be used to momentarily disable desired attractors from memory, hence biasing the search space to improve recall performance. This property allows control of chaotic wandering, favoring given subspaces over others. In addition, reinforcement learning can then enable a dual BAM architecture to store and recall nonlinearly separable patterns. Our results allow the same BAM framework to model three different types of learning: supervised, reinforcement, and unsupervised. This ability is very promising from the cognitive modeling viewpoint. The new BAM model is also useful from an engineering perspective; our simulations results reveal a notable overall increase in BAM learning and recall performances when using a hybrid model with the general regression neural network (GRNN).

Almost periodic solution to Cohen–Grossberg-type BAM networks with distributed delays

In this paper, a class of Cohen–Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is discussed. Based on inequality analysis method and combining the exponential dichotomy with fixed point theorem, some novel sufficient conditions are obtained to ensure the existence and globally exponential stability of almost periodic solution to this system. Moreover, an example is given to demonstrate the feasibility of our results.

On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching

In this paper, the stability analysis problem is investigated for stochastic bi-directional associative memory (BAM) neural networks with Markovian jumping parameters and mixed time delays. Both the global asymptotic stability and global exponential stability are dealt with. The mixed time delays consist of both the discrete delays and the distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the Lyapunov---Krasovskii stability theory and the Ito differential rule to establish sufficient conditions for the delayed BAM networks to be stochastically globally exponentially stable and stochastically globally asymptotically stable, respectively. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs). Therefore, the global stability of the delayed BAM with Markovian jumping parameters can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.

Optimal exponential synchronization of general chaotic delayed neural networks: An LMI approach

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Exponential stability of BAM neural networks with time-varying delays

In this paper, bi-directional associative memory (BAM) networks with time-varying delays are considered. By employing the homeomorphism theory, the idea of Lyapunov function and inequality technique, some new criteria are obtained to ensure the existence, uniqueness and global exponential stability of an equilibrium point. These results obtained are independent of delays, develop the existent outcome in the earlier literature

New delay-dependent exponential stability criteria of BAM neural networks with time delays

In this paper, the global exponential stability is investigated for the bi-directional associative memory networks with time delays. Several new sufficient conditions are presented to ensure global exponential stability of delayed bi-directional associative memory neural networks based on the Lyapunov functional method as well as linear matrix inequality technique. To the best of our knowledge, few reports about such “linearization” approach to exponential stability analysis for delayed neural network models have been presented in literature. The method, called parameterized first-order model transformation, is used to transform neural networks. The obtained conditions show to be less conservative and restrictive than that reported in the literature. Two numerical simulations are also given to illustrate the efficiency of our result.

Exponential stability of periodic solution to Cohen–Grossberg-type BAM networks with time-varying delays

Periodic solutions can represent various storage patterns or memory patterns in some applications. In this paper, the existence and global exponential stability of periodic solution are discussed for the Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with time-varying delays. By applying the analysis method and inequality technique, some novel sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and exponential stability of the periodic solution to the considered system. Moreover, two examples are also given to demonstrate the feasibility of the obtained results.

Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays

In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.

Global exponential stability of delayed BAM network on time scale

Some sufficient conditions are derived to ensure the global exponential stability of delayed bi-directional associative memory (BAM) neural network on time scale, using the time scale calculus theory and the Liapunov functional method. The conditions possess highly important significance and can be easily checked in practice by simple algebraic methods. This is the first time applying the time scale calculus theory to unify and improve discrete-time and continuous-time bi-directional associate memory neural network under the same framework.

Periodic oscillation for BAM neural networks with impulses

In this paper, a class of neural networks called bidirectional associative memory (BAM) networks with impulses is discussed. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution and the exponentially convergent rate is estimated. The sufficient conditions are easy to be verified and when the impulsive jumps are absent, the results reduce to those of the non-impulsive systems. The approaches are based on employing inequality analysis, matrix theory and its spectral theory.

Optimum associative neural network utilizing maximum likelihood

In this paper, a new learning rule and theoretical analysis of an extended bidirectional associative memory network (MLBAM) is presented, by using the maximum likelihood criterion based on two well recognized and essential criteria, i.e., the convergence of the learning rule, and the noise tolerance of this network. Traditional methods fail to distinguish highly approximative patterns. However, the method in our study can improve this by using the newly developed method of maximum likelihood criterion. To be specific, by employing the MLBAM, association and memory could be clearly distinguished. In addition, the learning approach guarantees that correlated patterns could be associated as a stable state and the network possesses excellent anti-noise property by using likelihood function, namely, the learning approach specializes in the situation including stochastic disturbance. Additionally, the associative capability of the bidirectional associative memory is specifically discussed. Finally, three experiments are used to certify the validity and efficiency of our method, especially the method's excellent anti-noise property by using likelihood function.

Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations

In this paper, we study a class of neural networks with discontinuous activations, which include bidirectional associative memory networks and cellular networks as its special cases. By the Leray–Schauder alternative theorem, matrix theory and generalized Lyapunov approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity.

Object recognition and tracking with maximum likelihood bidirectional associative memory networks

A maximum-likelihood-criterion based bidirectional associative memory network (hereinafter, the MLBAM network) is presented, which can be employed to evaluate the similarity between a template and a matching region. Furthermore, the analysis on the stability and the convergence of learning rule of the network is conducted. The results show that the MLBAM network is capable of associating two templates (big and small) and thus greatly reducing the computational load by using coarse-to-fine hierarchical strategy. Finally, an experiment on the target tracking of MLBAM network is conducted using a group of robots operating on a football field, demonstrating the high efficiency of the method.

Exponential synchronization of general chaotic delayed neural networks via hybrid feedback

This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, and covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, recurrent multilayer perceptrons (RMLPs). By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) technique, some exponential synchronization criteria are derived. Using the drive-response concept, hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria. Finally, detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Multistability in bidirectional associative memory neural networks

In this Letter, the multistability issue is studied for Bidirectional Associative Memory (BAM) neural networks. Based on the existence and stability analysis of the neural networks with or without delay, it is found that the 2 n-dimensional networks can have 3 n equilibria and 2 n equilibria of them are locally exponentially stable, where each layer of the BAM network has n neurons. Furthermore, the results has been extended to ( n + m ) -dimensional BAM neural networks, where there are n and m neurons on the two layers respectively. Finally, two numerical examples are presented to illustrate the validity of our results.

A unified treatment for stability preservation in computer simulations of impulsive BAM networks

This paper is concerned with the stability preservation in computer simulations of an impulsive bidirectional associative memory (BAM) network. The simulations are provided by difference equations formulated from a semi-discretisation technique and impulsive maps as discrete-time representations of the nonlinear impulses which attempt to destabilise the BAM network at fixed moments of time. Prior to producing the computer simulations, the analogue is analysed for its exponential convergence towards a unique equilibrium state. The analysis exploits the method of Lyapunov sequences to derive several sufficient conditions that govern the network parameters and the impulse magnitude and frequency. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. The treatment of the analysis leads us to a relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals.