Bidirectional Associative Memory Neural Networks Research Articles

Predefined-Time Synchronization of Stochastic Memristor-Based Bidirectional Associative Memory Neural Networks With Time-Varying Delays

In this article, we consider the predefined-time synchronization problem of stochastic memristor-based bidirectional associative memory neural networks (MBAMNNs). First, considering the influence of stochastic disturbance, we propose two new predefined-time theorems. Second, combined with the predefined-time theorem proposed in this article, we design a feedback controller to realize the predefined-time synchronization of MBAMNNs. Then, the sufficient conditions for the predefined-time synchronization of MBAMNNs are obtained based on Ito’s formula and Lyapunov theorem. Finally, the effectiveness of the theorems is verified by numerical simulations.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks

For a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay, we give sufficient conditions for its global asymptotic stability. The main stability criterion depends on the size of the delay on the linear part and the dominance of the linear terms over the nonlinear terms. We apply our main result to answer several open problems left by Berezansky et al. (2014). Using the obtained theoretical stability results, we get sufficient conditions for both the global asymptotic and global exponential stability of a bidirectional associative memory neural network model with delays which generalizes models recently studied. Finally, a numerical example is given to illustrate the novelty of our results.

Braille–Latin conversion using memristive bidirectional associative memory neural network

Braille–Latin conversion using memristive bidirectional associative memory neural network

Global exponential p-norm stability of BAM neural networks with unbounded time-varying delays: A method based on the representation of solutions

This paper studies the global exponential [Formula: see text]-norm stability of bidirectional associative memory (BAM) neural networks with unbounded time-varying delays. A novel method based on the representation of solutions is put forward to deduce a global exponential [Formula: see text]-norm stability criterion. This method does not need to set up any Lyapunov–Krasovskii functionals (LKF), which can greatly reduce a large amount of computations and is simpler than the existing methods. In the end, representative numerical examples are given to illustrate the availability of the method.

H∞ State Estimation for BAM Neural Networks With Binary Mode Switching and Distributed Leakage Delays Under Periodic Scheduling Protocol.

This article is concerned with the H∞ state estimation problem for a class of bidirectional associative memory (BAM) neural networks with binary mode switching, where the distributed delays are included in the leakage terms. A couple of stochastic variables taking values of 1 or 0 are introduced to characterize the switching behavior between the redundant models of the BAM neural network, and a general type of neuron activation function (i.e., the sector-bounded nonlinearity) is considered. In order to prevent the data transmissions from collisions, a periodic scheduling protocol (i.e., round-robin protocol) is adopted to orchestrate the transmission order of sensors. The purpose of this work is to develop a full-order estimator such that the error dynamics of the state estimation is exponentially mean-square stable and the H∞ performance requirement of the output estimation error is also achieved. Sufficient conditions are established to ensure the existence of the required estimator by constructing a mode-dependent Lyapunov-Krasovskii functional. Then, the desired estimator parameters are obtained by solving a set of matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the proposed estimator design method.

Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks

In this paper, a new case of neural networks called fractional-order octonion-valued bidirectional associative memory neural networks (FOOVBAMNNs) is established. First, the higher dimensional models are formulated for FOOVBAMNNs with general activation functions and the special linear threshold ones, respectively. On one hand, employing Cayley–Dichson construction in octonion multiplication which is essentially neither commutative nor associative, the system of FOOVBAMNNs is divided into four fractional-order complex-valued ones. On the other hand, Caputo fractional derivative’s character and BAM’s interactive feature are also properly dealt with. Second, the general criteria are obtained by the new design of LKFs, the application of the related inequalities and the construction of the linear feedback controllers for the global Mittag-Leffler synchronization problem of FOOVBAMNNs. Finally, we present two numerical examples to show the realizability and progress of the derived results.

Finite-time dissipative control for bidirectional associative memory neural networks with state-dependent switching and time-varying delays

This paper focuses on finite-time exponential dissipative analysis and control problems for bidirectional associative memory neural networks (BAMNNs) with state-dependent switching and time-varying delays. Firstly, the state-dependent switching parameters of BAMNNs are interpreted as interval parameters by the interval matrix method instead of differential inclusion theory and set-value map. Under the framework of Filippov’s solution and differential inclusions, some sufficient conditions of finite-time bounded (FTB) and finite-time exponential (Q,S,R)−γ dissipative (FTED) for BAMNNs are obtained based on Lyapunov–Krasovskii functional (LKF) and some inequality techniques. Then, the finite-time dissipative PI controllers are designed by solving linear matrix inequality (LMI). Finally, a numerical example is given to illustrate the correctness of the proposed results and the effectiveness of the designed controllers.

Novel Global Asymptotic Stability and Dissipativity Criteria of BAM Neural Networks With Delays

In this article, issues of both stability and dissipativity for a type of bidirectional associative memory (BAM) neural systems with time delays are investigated. By using generalized Halanay inequalities and constructing appropriate Lyapunov functionals, some novelty criteria are obtained for the asymptotic stability for BAM neural systems with time delays. Also, without assuming boundedness and differentiability for activation functions, some new sufficient conditions for proving the dissipativity are established by making use of matrix theory and inner product properties. The received conclusions extend and improve some previously known works on these problems for general BAM neural systems. In the end, numerical simulation examples are made to show the availability of the theoretical conclusions.

Event-triggered hybrid impulsive control on lag synchronization of delayed memristor-based bidirectional associative memory neural networks for image hiding

Memristor-based bidirectional associative memory neural networks (MBAMNNs) analysis can help to reveal the dynamic basis of secure communication. Effectively representing the synchronization of MBAMNNs is the principal task of applying brain-inspired neural networks to image hiding. Previous research has typically utilized continuous control methods to represent the synchronization of MBAMNNs, but these are not well coordinated under limited network bandwidth. Besides, the special communication features and uncertainties of MBAMNNs will affect the image encryption/decryption by introducing the concept of chaos synchronization for image hiding, but few studies have explored such elements. To address these two issues, we propose an event-triggered hybrid impulsive scheme on lag synchronization for image hiding. Specifically, we incorporate both time-varying uncertainties and the multi-layer topology structure of MBAMNNs into a designed event-triggered scheme. The frequency of the controller can be automatically updated from two novel triggered conditions, and Zeno-behavior can be avoided effectively. Experimental results demonstrate that our scheme not only outperforms several exciting approaches in synchronization but also can effectively realize the image hiding under low energy consumption.

Further analysis on dynamical properties of fractional‐order bi‐directional associative memory neural networks involving double delays

In this study, a class of novel fractional‐order bi‐directional associative memory (BAM) neural networks involving double time delays are put up and investigated. First of all, we prove that the solution of the involved neural networks exists and is unique and bounded. Second of all, we investigate the stability behavior and the onset of Hopf bifurcation of the involved network models by applying the stability theory and the related Hopf bifurcation knowledge on fractional‐order differential equations. A sufficient condition to ensure the stability and onset of Hopf bifurcation of the considered network models is established. The importance of time delay in dynamical behavior of the fractional‐order delayed BAM neural networks has been displayed. Lastly, computer simulations with Matlab software are presented to test the effectiveness of the established theoretical results. The obtained analysis fruits of this manuscript play a vital role in designing and controlling networks.

A new predefined-time stability theorem and its application in the synchronization of memristive complex-valued BAM neural networks

In this paper, two novel and general predefined-time stability lemmas are given and applied to the predefined-time synchronization problem of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs). Firstly, different from the generally fixed-time stability lemma, the setting of an adjustable time parameter in the derived predefined-time stability lemma causes it to be more flexible and more general. Secondly, the model studied in the complex-valued BAM neural networks model, which is different from the previous discussion of the real part and imaginary part respectively. It is more practical to study the complex-valued nonseparation. Thirdly, two effective controllers are designed to realize the synchronization performance of BAM neural networks based on the predefined-time stability, and the analysis is given based on general predefined-time synchronization. Finally, the correctness of the theoretical derivation is verified by numerical simulation. A secure communication scheme based on predefined-time synchronization of MCVBAMNNs is proposed, and the effectiveness and superiority of the results are proved.

Global [formula omitted]-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control

This article deals with global μ-stabilization of quaternion-valued inertial bidirectional associative memory neural networks (QVIBAMNNs) with time-varying delays via time-delayed impulsive control. Firstly, the existence and uniqueness of the equilibrium point are proved by the homeomorphism mapping method. Then, based on an improved differential inequality, sufficient conditions for global μ-stabilization of QVIBAMNNs via time-delayed impulsive control are obtained. Significantly, the activation function in this paper is an extension of Lipschitz condition, which is superior to general quaternion-valued activation function. And quaternion is not required to be decomposed into real or complex values in this paper. Ultimately, some numerical simulations have proved the feasibility of the theorems.

Mittag–Leffler Synchronization of Caputo-Delayed Quaternion BAM Neural Networks via Adaptive and Linear Feedback Control Designs

The Mittag–Leffler synchronization (MLS) issue for Caputo-delayed quaternion bidirectional associative memory neural networks (BAM-NNs) is studied in this paper. Firstly, a novel lemma is proved by the Laplace transform and inverse transform. Then, without decomposing a quaternion system into subsystems, the adaptive controller and the linear controller are designed to realize MLS. According to the proposed lemma, constructing two different Lyapunov functionals and applying the fractional Razumikhin theorem and inequality techniques, the sufficient criteria of MLS on fractional delayed quaternion BAM-NNs are derived. Finally, two numerical examples are given to illustrate the validity and practicability.

Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays

This article aims to deal with the stability and Hopf bifurcation analysis for a type of fractional-order bidirectional associative memory (BAM) neural network involving two neurons in the X-layer and n neurons in the Y-layer, respectively. In view of the universal existence and multiplicity of time delay in many real systems, leakage delay and nonuniform communication delays are both taken into account. Coates’s flow-graph formula is efficiently adopted to solve the high-order characteristic equation of the associated linearized system. By making some assumptions on the mixed time delays, the obtained characteristic equation only contains the leakage delay, which is selected as the bifurcation parameter. Utilizing the discriminated criteria of stability for fractional-order dynamical systems and Hopf bifurcation theory, we obtain the critical value of the bifurcation point, greater than which the Hopf bifurcation would occur. Particularly, the stability and Hopf bifurcation is also analyzed for the case of no leakage delay to get an insight into the effect of the leakage delay. Finally, the validity of our theoretical results is substantiated through a simulation example.

Passivity Analysis of Fractional-Order Neutral-Type Fuzzy Cellular BAM Neural Networks with Time-Varying Delays

In this paper, passivity analysis of fractional-order neutral-type fuzzy cellular bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for solvability of the passive problem are obtained in terms of linear matrix inequalities (LMIs), which can be easily checked by using the MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results.

Robust Stability of Fractional Order Memristive BAM Neural Networks with Mixed and Additive Time Varying Delays

This paper is concerned with the problem of the robust stability of fractional-order memristive bidirectional associative memory (BAM) neural networks. Based on Lyapunov theory, fractional-order differential inequalities and linear matrix inequalities (LMI) are applied to obtain a robust asymptotical stability. Finally, numerical examples are presented.

Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis

In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.

Event-Triggered Hybrid Impulsive Control on Lag Synchronization of Delayed Memristor-Based Bidirectional Associative Memory Neural Networks for Image Hiding

Event-Triggered Hybrid Impulsive Control on Lag Synchronization of Delayed Memristor-Based Bidirectional Associative Memory Neural Networks for Image Hiding

Impulsive effects on stochastic bidirectional associative memory neural networks with reaction-diffusion and leakage delays

In this paper, the problem of global asymptotic stability analysis for stochastic reaction-diffusion bidirectional associative memory neural networks (BAMNNs) with mixed delays and impulsive effects are investigated. The mixed delays consists of time delays in the leakage terms and continuously distributed delays. Based on the Lyapunov–Krasovskii functional (LKF), It's differential formula and linear matrix inequality (LMI) method, some sufficient conditions for global asymptotic stability in mean square of the equilibrium point of the systems are derived. The feasibility of the conditions are verified using the MATLAB LMI toolbox. Finally, two examples are provided to illustrate the effectiveness and validity of the derived main results.