Bidirectional Associative Memory Neural Networks Research Articles

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

Bidirectional associative memory models are 2‐layer heteroassociative networks. In this work, we prove the existence and the global exponential stability of the unique weighted pseudo–almost periodic solution of bidirectional associative memory neural networks with mixed time‐varying delays and leakage time‐varying delays on time‐space scales. Some sufficient conditions are given for the existence, the convergence, and the global exponential stability of the weighted pseudo–almost periodic solution by using fixed‐point theorem and differential inequality techniques. The results of this paper complement the previous outcomes. An example is given to show the effectiveness of the derived results via computer simulations.

Mittag-Leffler stability of impulsive fractional-order bi-directional associative memory neural networks with time-varying delays

In the paper, a class of impulsive Caputo fractional-order bi-directional associative memory neural networks with time-varying delays is considered. Applying the fractional Lyapunov method, a sufficient condition for Mittag-Leffler stability of the equilibrium point of the system under consideration is derived. Some earlier results are extended and improved. Our results provide an impulsive control law which stabilizes the impulse-free fractional-order neural network time-delay model. An example is provided to demonstrate the effectiveness of the proposed results.

Asymptotic and Robust Mean Square Stability Analysis of Impulsive High-Order BAM Neural Networks with Time-Varying Delays

In this paper, the globally asymptotical stability in the mean square for a class of high-order bidirectional associative memory neural networks with time-varying delays and fixed moments of impulsive effect are studied. The proof makes use of Lyapunov–Krasovskii functionals, and the conditions are expressed in terms of linear matrix inequalities. A controller has been derived to robustly stabilize this network. Two illustrative examples are also given at the end of this paper to show the effectiveness of our results.

Exponential dissipativity criteria for generalized BAM neural networks with variable delays

This article evaluates the exponential dissipativity and passivity criterions for generalized bidirectional associative memory neural networks (BAMGNNs) including interval time-varying delayed signals. Exponential dissipativity and passivity criterions are proposed by making suitable Lyapunov–Krasovskii functional and proposing a novel approach. The improved reciprocally convex combination and weighted integral inequality techniques are utilized to obtain new exponential dissipativity and passivity conditions of such delayed BAMGNNs. The feasibility of the obtained results is clearly demonstrated by numerical examples.

Exponential input-to-state stability for complex-valued memristor-based BAM neural networks with multiple time-varying delays

Abstract In this paper, the exponential input-to-state stability (ISS) for complex-valued memristor-based bidirectional associative memory (BAM) neural networks with multiple time-varying delays is discussed. By constructing a novel Lyapunov functional and utilizing inequality techniques, a sufficient criterion of the exponential input-to-state stability for the considered system is firstly derived. Moreover, similar result is also obtained for delayed complex-valued BAM neural networks without memristors. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.

On the Weighted Pseudo-Almost Periodic Solution for BAM Networks with Delays

In this paper, a class of Bidirectional Associative Memory neural networks with time-varying weights and continuously distributed delays is discussed. Sufficient conditions are obtained for the existence and uniqueness of weighted pseudo-almost periodic solution of the considered model and numerical examples are given to show the effectiveness of the obtained results.

Delay prediction algorithm based on bidirectional associative memory neural network

In this paper, a delay prediction algorithm based on bidirectional associative memory neural network is proposed. The algorithm firstly uses RTT similarity to define and establish the delay function of router processing. Then, the random coefficient and other parameters of uncertain factors such as network congestion rate and network delay are calculated, to establish the prediction model of network delay. Then, the bidirectional associative memory neural network algorithm is combined with the normal distribution, and the obtained model is input to get the network delay law. The experimental results show that the proposed algorithm can predict the network delay with high accuracy, and is a feasible prediction algorithm.

Dissipativity and Synchronization of Generalized BAM Neural Networks With Multivariate Discontinuous Activations.

This paper is concerned with the dissipativity and synchronization problems of a class of delayed bidirectional associative memory (BAM) neural networks in which neuron activations are modeled by discontinuous bivariate functions. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides and mixed delays via functional differential inclusions. The global dissipativity of the Filippov solution to the considered BAM neural networks is proven using generalized Halanay inequalities and matrix measure approaches. Second, to realize global exponential complete synchronization of BAM neural networks with multivariate discontinuous activations, discontinuous state feedback controllers are designed using functional differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov functional method. Finally, several numerical examples are provided to demonstrate the applicability and effectiveness of our proposed results.

Reachable set estimation for inertial Markov jump BAM neural network with partially unknown transition rates and bounded disturbances

This paper mainly focuses on the reachable set estimation problem of a time-varying delayed inertial Markov jump bidirectional associative memory (BAM) neural network with bounded disturbance inputs. The disturbances are assumed to be either unit-energy bounded or unit-peak bounded. Different from systems of the past studies, this paper is for inertial Markov jump BAM neural network with both time-varying delay and time-varying transition rates. The time-varying character of the considered transition rates is assumed to be piecewise-constant. In order to reduce the conservatism, the delay-partitioning technique is utilized to solve this reachable set estimation problem. As a result, it is obtained that the ellipsoid defined in this paper contains the reachable set Rup, which indicates the reachable set Rue is included. Further, we extend the results to the uncertain Markov jump BAM neutral network with partially unknown transition probabilities. Numerical examples are proposed to show the effectiveness of the given results.

Global Exponential Stability of Impulsive Fuzzy High-Order BAM Neural Networks With Continuously Distributed Delays.

This paper investigates the stability of equilibrium point and periodic solution for impulsive fuzzy high-order bidirectional associative memory neural networks with continuously distributed delays. By applying the inequality analysis technique, -matrix, and Banach contraction mapping principle and constructing some suitable Lyapunov functionals, some sufficient conditions for the uniqueness and global exponential stability of equilibrium point and global exponential stability of periodic solutions are established. In addition, three examples with numerical simulations are presented to demonstrate the feasibility and effectiveness of the theoretical results.

Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

In this paper, the global asymptotic stability of memristive bidirectional associative memory neural networks with leakage delay and two additive time-varying delays is firstly studied. Then, we propose a novel sampled-data feedback controller to guarantee the synchronization of system based on drive/response concept. In particular, taking full advantage of the input delay approach, the Lyapunov function method and the Jensen’s inequality theory, several sufficient conditions are obtained. Finally, two numerical simulation examples show the effectiveness of the designed sampled-data control strategy. Furthermore, our results can be applied to simulate the associative memory function of brain-like robots, large-scale information storage, etc.

Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes.

This paper is concerned with the drive-response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

Adaptive synchronization between two non-identical BAM neural networks with unknown parameters and time-varying delays

In this paper, the synchronization of two non-identical bidirectional associative memory (BAM) neural networks with unknown parameters and time-varying delays is investigated. Two adaptive controllers are designed to guarantee the global asymptotic synchronization of state trajectories for two non-identical BAM neural networks. Lyapunov stability theory and Barbalat’s lemma are used to guarantee the synchronization of response and drive systems. Finally, an illustrative example is given to demonstrate the effectiveness of the presented synchronization scheme.

Stability of nonlinear Volterra equations

AbstractUsing a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales

In this paper, by applying the exponential dichotomy theory on time scales, Banach contraction mapping principle and differential inequality analysis techniques, we establish some sufficient conditions for the existence and global exponential stability of almost automorphic solution for neutral type high-order Hopfield bidirectional associative memory (BAM) neural networks with time-varying leakage delays on time scales. In the addressed system, we not only consider the effects of the first-order neutral terms on networks, but also investigate the influences of the second-order neutral terms on the networks. High-order Hopfield BAM neural networks with continuously distributed leakage delays on time scales are also considered. Our results are completely new even if time scale T=R or T=Z and complementary to the previously existing results. Finally, three examples with numerical simulations are presented to illustrate the feasibility of our proposed theoretical results.

Global Stability and Bifurcation in Delayed Bidirectional Associative Memory Neural Networks With an Arbitrary Number of Neurons

In this paper, delayed bidirectional associative memory (BAM) neural networks, which consist of one neuron in the X-layer and other neurons in the Y-layer, will be studied. Hopf bifurcation analysis of these systems will be discussed by proposing a general method. In fact, a general n-neuron BAM neural network model is considered, and the associated characteristic equation is studied by classification according to n. Here, n can be chosen arbitrarily. Moreover, we find an appropriate Lyapunov function that under a hypothesis, results in global stability. Numerical examples are also presented.

Mittag–Leffler Stability and Global Asymptotically $$\omega $$ ω -Periodicity of Fractional-Order BAM Neural Networks with Time-Varying Delays

This article studies the Mittag–Leffler stability and global asymptotical $$\omega $$ -periodicity for a class of fractional-order bidirectional associative memory (BAM) neural networks with time-varying delays by using Laplace transform, stability theory of fractional systems and some integration technique. Firstly, some sufficient conditions are given to ensure the boundedness and global Mittaag-Leffler stability of fractional-order BAM neural networks with time-varying delays. Next, S-asymptotical $$\omega $$ -periodicity and global asymptotical $$\omega $$ -periodicity of fractional-order BAM neural networks with time-varying delays are also explored. Finally, some numerical examples and simulation are performed to show the effectiveness of theoretical results.

Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays

This article explores the exponential stability problem of complex-valued bidirectional associative memory (BAM) neural networks with time delays. This analysis is on the basis of the M-matrix approach, the differential inclusions theory and the homeomorphism property. By constructing a novel Lyapunov functional, a sufficient criterion for the existence, uniqueness, and exponential stability for the equilibrium point of the considered system is derived. Moreover, similar results in terms of M-matrix are also obtained for the exponential stability problem of delayed complex-valued BAM neural networks without memristors. In the end, two numerical examples are provided to demonstrate the availability of the obtained results.

Dissipativity analysis of complex-valued BAM neural networks with time delay

This paper is concerned with dissipativity analysis of complex-valued bidirectional associative memory (BAM) neural networks (NNs) with time delay. Some novel sufficient conditions that guarantee the dissipativity of complex-valued BAM neural networks (CVBNNs) are obtained by using the inequality techniques, Halanay inequality, and upper right Dini derivative concepts. The complex-valued nonlinear function is separated into its real and imaginary parts to a set of sufficient conditions for the global dissipativity of CVBNNs by using the matrix measure method. Moreover, the global attractive sets are obtained, which are positive invariant sets. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed theoretical results.

The Sampled-data Exponential Stability of BAM with Distributed Leakage Delays

This paper investigates the exponential stability of bidirectional associative memory (BAM) neural networks with distributed leakage delays and sampled-data state feedback input. Based on the input delay approach, the considered BAM neural networks is transformed into a system with mixed distributed leakage delays and time-varying discrete delays. Some sufficient conditions are given to ensure that the system is exponentially stable. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical analysis.