Bidirectional Associative Memory Neural Networks Research Articles

Input-to-state stability analysis for memristive BAM neural networks with variable time delays

In this paper, we are concerned with input-to-state stability of a class of memristive bidirectional associative memory (BAM) neural networks with variable time delays. Based on a nonsmooth analysis and set-valued maps, some novel sufficient conditions are obtained for the input-to-state stability of such networks, which extended some known results as particular cases. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of our results.

Influence of Time Delay on Bifurcation in Fractional Order BAM Neural Networks With Four Delays

Over the past several decades, numerous scholars have studied the stability and Hopf bifurcation problem of integer-order delayed neural networks. However, the fruits about the stability and Hopf bifurcation for fractional-order delayed neural networks are very scarce. In this paper, we will consider the stability and the existence of Hopf bifurcation of fractional-order bidirectional associative memory (BAM) neural networks with four delays. A set of sufficient criteria to ensure the stability and the existence of Hopf bifurcation for the fractional-order BAM neural networks with four delays are established by choosing the sum of two different delays as a bifurcation parameter. This paper manifests that the delay has an important influence on the stability and Hopf bifurcation of involved networks. An example is displayed to test the rationality of the derived theoretical findings. The derived results of this paper are new and play a key role in optimizing networks and improving human life.

Anti-periodic solutions for fractional-order bidirectional associative memory neural networks with delays

This paper concerns fractional-order bidirectional associative memory neural networks with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions are established. An example is given to show the feasibility main results.

Stability Analysis of Fractional‐Order Bidirectional Associative Memory Neural Networks with Mixed Time‐Varying Delays

This paper studies the stability analysis of fractional‐order bidirectional associative memory neural networks with mixed time‐varying delays. The orders of these systems lie in the interval (1,2). Firstly, a sufficient condition is derived to ensure the finite‐time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

Lagrange Exponential Stability of Complex-Valued BAM Neural Networks With Time-Varying Delays

This paper is concerned with the Lagrange exponential stability problem of complex-valued bidirectional associative memory neural networks with time-varying delays. On the basis of activation functions satisfying different assumption conditions, by combining the Lyapunov function approach with some inequalities techniques, different sufficient criteria including algebraic conditions and the condition in terms of LMI are derived to guarantee Lagrange exponential stability of the addressed system, respectively. Moreover, the estimations of different globally attractive sets named the convergence balls are also provided. In the end, the effectiveness and superiority–inferiority of these different results are verified by illustrative examples.

Anti-Synchronization for Complex-Valued Bidirectional Associative Memory Neural Networks With Time-Varying Delays

Anti-Synchronization for Complex-Valued Bidirectional Associative Memory Neural Networks With Time-Varying Delays

Finite-time stabilization of fractional-order delayed bidirectional associative memory neural networks

Finite-time stabilization of fractional-order delayed bidirectional associative memory neural networks

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

Stability Analysis for a Class of Impulsive Bidirectional Associative Memory (BAM) Neural Networks with Distributed Delays and Leakage Time-Varying Delays

In this paper, by employing contraction mapping principle theorem and by finding suitable Lyapunov–Krasovskii functional, some sufficient conditions are given for the existence and the global exponential stability, the uniform asymptotic stability, the global asymptotic stability and the uniform stability of the unique equilibrium point of bidirectional associative memory neural networks with distributed delays and leakage time-varying delays. Three illustrative examples are given at the end of this paper to demonstrate the effectiveness of our theoretical results.

Discrete Fractional‐Order BAM Neural Networks with Leakage Delay: Existence and Stability Results

AbstractIn this paper, a discrete model of fractional‐order bidirectional associative memory (BAM) neural networks with leakage delay is considered. Sufficient conditions are established for the existence, uniqueness and uniform stability of nontrivial solutions of the addressed model. Our approach is based on the implementation of the newly defined discrete fractional calculus, mathematical inequalities and fixed point theorems. We provide an example that supports the application of the theoretical results.

Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays

In this paper, stochastic stability of neutral type Markovian-jumping bidirectional associative memory (BAM) neural networks is investigated. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. The activation functions are supposed to be bounded and globally Lipschitz continuous. Furthermore, based on the Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions and novel delay-dependent conditions are established for the stochastic asymptotic stability of Markovian jumping BAM neural networks. The condition is presented in terms of linear matrix inequalities (LMIs), which can be easily checked by using MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results.

Global asymptotic stability of a class of generalized BAM neural networks with reaction-diffusion terms and mixed time delays

Abstract In this paper, a novel linear matrix inequality (LMI)-based sufficient condition, which guarantees the existence and global asymptotic stability of a class of generalized bidirectional associative memory (BAM) neural networks with reaction-diffusion terms and mixed time delays, is obtained by using inequality technique, degree theory, LMI method and constructing Lyapunov functional. The mixed time delays consist of both the discrete delays and the infinitely distributed delays. The results generalize and improve the earlier publications under the assumption that the activation functions only satisfy general global Lipschitz conditions. Two simple examples are provided to demonstrate the effectiveness of the proposed theoretical results. These results can be applied to design globally asymptotically stable networks and thus have important significance in both theory and applications.

Asymptotic anti-synchronization of memristor-based BAM neural networks with probabilistic mixed time-varying delays and its application

This paper is concerned with the asymptotic anti-synchronization problem of the memristor-based bidirectional associative memory neural networks (MBAMNNs) and its application in network secure communication. First, we propose a new model of MBAMNNs with probabilistic delays. By establishing a Bernoulli distributed stochastic variable, the information of transmittal time-varying delays is studied. Second, in order to provide a more robust and secure system, we develop a new anti-synchronization model based on the MBAMNNs. The adaptive laws are carefully designed to confirm the process of encryption and decryption in networks secure communication system. Finally, several numerical examples are presented to demonstrate the effectiveness and applicability of our proposed mechanism.

Finite‐time synchronization for memristor‐based BAM neural networks with stochastic perturbations and time‐varying delays

SummaryThis paper focuses on the finite‐time synchronization issue of drive‐response memristor‐based bidirectional associative memory neural networks (MBAMNNs) with stochastic perturbations and time‐varying delays. Based on the mathematical model of memristor, definition of finite‐time stability for stochastic differential system and the drive‐response concept, some novel sufficient conditions are given to ensure the finite‐time synchronization of drive‐response MBAMNNs with stochastic perturbations and time‐varying delays. We design novel nonlinear feedback controllers to control the synchronization error to converge zero in a finite time, and the settling time for synchronization can be easily obtained. In addition, as two special cases, the finite‐time synchronization control criteria for bidirectional associative memory neural networks with stochastic perturbations and time‐varying delays and MBAMNNs without stochastic perturbations are also given. Finally, two numerical simulations are showed to demonstrate the correctness of main results.

Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays

In this paper, we are concerned with the master-slave synchronization problem of fractional-order three-neuron bidirectional associative memory (BAM) neural networks with multiple time delays. The linear feedback controller is designed to ensure the global synchronization of the master-slave systems. Based on the Lyapunov functionals and fractional-order comparison theory, the corresponding synchronization conditions are derived. In the end, an example is given to further demonstrate the effectiveness of the obtained results.

$$(\mu ,\nu )$$(μ,ν)-Pseudo-almost automorphic solutions for high-order Hopfield bidirectional associative memory neural networks

This article is concerned with a high-order Hopfield bidirectional associative memory neural networks with time-varying coefficients and mixed delays. Sufficient conditions are derived for the existence, the uniqueness and the exponential stability of $$(\mu ,\nu )$$-pseudo-almost automorphic solutions of the considered model. Banach fixed-point theorem is applied for the existence and the uniqueness results. Global exponential stability is derived via differential inequalities. Finally, two examples are provided to support the feasibility of the theoretical results.

An audio encryption based on synchronization of robust BAM FCNNs with time delays

In this work, authors’ proposed an audio encryption based on synchronization of hybrid bidirectional associative memory (BAM) and fuzzy cellular neural networks (FCNNs) with time delays. Here, the significant effort is to find the values of the parameters $A,\ B,\ D,\ \alpha ,\ \beta ,\ \tilde {A},\ \tilde {B},\ \tilde {D},\ \tilde {\alpha },\ \tilde {\beta },\ L,\ \tilde {L},$ $O_{d}, \ \tilde {O}_{d},\ O_{a}, \ \tilde {O}_{a},\ O_{b}, \ \tilde {O}_{b},$ of the given robust BAM FCNNs system to obtain the dynamical signal (chaotic) which are used to encrypt an audio file and satisfy the condition of Linear matrix inequality (LMI) by choosing suitable Lyapunov-Krasovskii functional (LKF). Further, the key sensitivity of order $10^{-10}$ of this proposed method have massive key space to make brute-force attack infeasible. Numerical simulations, results and discussions along with comparison are provided to illustrate the effectiveness and merits of the proposed scheme.

Bidirectional Associative Memory Neural Network for Data Encryption and Decryption

Bidirectional Associative Memory Neural Network for Data Encryption and Decryption

Finite-time anti-synchronization of memristive stochastic BAM neural networks with probabilistic time-varying delays

This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism.

General decay synchronization of delayed BAM neural networks via nonlinear feedback control

This paper studies the general decay synchronization of a class of bidirectional associative memory neural networks with time-varying delays. First, a useful lemma which generalizes the classical exponential synchronization and polynomial synchronization is introduced. Then by using this lemma, some simple sufficient criteria ensuring the general decay synchronization of considered bidirectional associative memory neural networks are obtained via designing a novel nonlinear feedback controller and using some inequality techniques. Finally, two numerical examples are provided to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization.