Associative Memory Neural Networks Research Articles

Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

SummaryIn real‐world problems, neural networks play an increasingly important role in terms of both theory and applications. In this paper, the asymptotic stability analysis issue is investigated for uncertain impulsive discrete‐time bidirectional associative memory neural networks with leakage and time‐varying delays. With the assistance of novel summation inequality, reciprocally convex combination technique, and triple Lyapunov‐Krasovskii functionals terms, many cases of time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainty, and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. An important feature of the results reported here is that the probability of occurrence of the parameter uncertainties specify a priori estimate. Finally, numerical examples are proposed to expose the capability and efficiency of our research work with the help of the LMI control toolbox in MATLAB.

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

SummaryThis paper presents a global exponential stability of antiperiodic solution for a class of impulsive discrete‐time Markovian jumping stochastic bidirectional associative memory neural networks with additive time‐varying delays and leakage delay. By utilizing the Lyapunov‐Krasovskii functional and contraction mapping principle, several sufficient conditions and linear matrix inequalities are derived for verifying globally exponentially stable in the mean square. There is a new delay‐dependent criterion for checking the existence, uniqueness, and global stability for antiperiodic solution. Meantime, by using the numerically efficient MATLAB Toolbox, simulation examples are offered to show the effectiveness and usefulness of the obtained result.

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results

Anti-periodic oscillations of bidirectional associative memory (BAM) neural networks with leakage delays

In this article, we discuss anti-periodic oscillations of BAM neural networks with leakage delays. A sufficient criterion guaranteeing the existence and exponential stability of the involved model is presented by utilizing mathematic analysis methods and Lyapunov ideas. The theoretical results of this article are novel and are a key supplement to some earlier studies.

Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]

Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control

This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Pseudo Almost Periodic Solutions for MAMs with an Oscillating Coefficient and Distributed Delays

This paper concerns with the pseudo almost periodic solutions for a multidirectional associative memory neural network with an oscillating coefficient and distributed delays. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions for the model considered in this work, which complement with all results in Zhou et al. (Math Comput Simul 107:52–60, 2015). Moreover, an example and its numerical simulation are given to support the theoretical results.

21aWA-2 シナプスノイズのある連想記憶モデルの系統的特長付け(情報統計力学,領域11,統計力学,物性基礎論,応用数学,力学,流体物理)

21aWA-2 シナプスノイズのある連想記憶モデルの系統的特長付け(情報統計力学,領域11,統計力学,物性基礎論,応用数学,力学,流体物理)

Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays

In this paper, a class of simplified bidirectional associative memory (BAM) neural networks with multiple delays are considered. By analyzing the associated characteristic transcendental equation, their linear stability is investigated and Hopf bifurcation is demonstrated. By applying Nyquist criterion, the length of delay which preserves the stability of the zero equilibrium is estimated. Some explicit results are derived for stability and direction of the bifurcating periodic orbit by using the normal form theory and center manifold arguments. Global existence of periodic orbits is also established by using a global Hopf bifurcation theorem for functional differential equations (FDE) and a Bendixson’s criterion for high-dimensional ordinary differential equations (ODE) due to Li and Muldowney. Finally, numerical simulations supporting the theoretical analysis are carried out.

Fuzzy modelling and model reference neural adaptive control of the concentration in a chemical reactor (CSTR)

This simulation study is a fuzzy model-based neural network control method. The basic idea is to consider the application of a special type of neural networks based on radial basis function, which belongs to a class of associative memory neural networks. The novelty of this approach is the use of an RBF neural network controller in a model reference adaptive control architecture, based on a one-step-ahead Takagi–Sugeno fuzzy model. The objective is to control the concentration in a continuous stirred-tank reactor highly non-linear system and to assure its stability by limiting the temperature rise generated from the irreversible exothermic reaction. This contribution will help to reduce environmental impact of chemical waste.

Passivity of memristive BAM neural networks with leakage and additive time-varying delays

This paper investigates the passivity of memristive bidirectional associate memory neural networks (MBAMNNs) with leakage and additive time-varying delays. Based on some useful inequalities and appropriate Lyapunov–Krasovskii functionals (LKFs), several delay-dependent conditions for passivity performance are obtained in linear matrix inequalities (LMIs). Moreover, the leakage delays as well as additive delays are considered separately. Finally, numerical simulations are provided to demonstrate the feasibility of the theoretical results.

Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters

This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples.

Finite-Time Synchronization of Chaotic Memristive Multidirectional Associative Memory Neural Networks and Applications in Image Encryption

Traditional biological neural networks lack the capability of reflecting variable synaptic weights when simulating associative memory of human brains. In this paper, we propose a novel memristive multidirectional associative memory neural networks (MAMNNs) model with mixed time-varying delays. More precisely, the proposed model is investigated with time-varying delays and distributed delays. Then, we design two kinds of delay-independent and delay-dependent controllers to analyze the problem of finite-time synchronization. Based on the drive-response concept and Lyapunov function, some sufficient criteria guaranteeing the finite-time synchronization of the drive-response system are derived. With the removal of certain constraints on the weight parameters, the results we obtained for synchronization are less conservative. To illustrate the chaotic characteristics of the memristive MAMNNs, an image encryption scheme is designed. Meanwhile, the effectiveness of the proposed theories is validated with numerical experiments.

Finite-Time Projective Synchronization of Memristor-Based BAM Neural Networks and Applications in Image Encryption

Inspired by security applications in the image transmission, this paper focuses on the usage of chaotic properties of memristor-based bidirectional associate memory neural networks (MBAMNNs) for image encryption against illegal attack. A class of memristor-based bidirectional associate memory neural networks with delays and stochastic perturbations is formulated and analyzed. Based on drive-response concept, Ito’s differential formula and inequality technique, some sufficient criteria are obtained to guarantee the finite-time projective synchronization. In order to realize the image encryption, we propose a chaotic color image encryption algorithm based on MBAMNNs. Illustrative examples are provided to verify the developed finite-time projective synchronization results. And we also show the great chaotic properties of the models proposed in this paper. Analysis of the encryption effect demonstrated the security of the proposed image encryption algorithm, and the potential applications of our models in secure image transmission are analyzed.

A Memristive Neural Network Model With Associative Memory for Modeling Affections

Memristor is a nonlinear resistor with memory, which has the characteristics of neuron synapses and can be used to design a new generation of memristive neural networks. Based on the Pavlov associative memory, a novel memristive associative memory neural network model is designed by using the charge-controlled nanoscale HP memristor model as the electronic synapse. This model includes neurons, memristor synapses, and weighted input feedback learning rule. Based on the proposed memristive associative memory model, a memristor-based neural network structure for simulating human emotions is further designed. The emotion simulation takes into account the excitation and inhibition between different neurons, making it more bionic. In order to simulate the memristive neural network structure, a relatively simplified emotional simulation circuit is constructed, which effectively reduces the network complexity and circuit power consumption. Finally, PSPICE is used to simulate the circuit. The simulation results not only verify the correctness of the model but also achieve a simple simulation of human emotions, which is helpful for the further development of the artificial neural network in the field of artificial intelligence.

Passivity of Memristive BAM Neural Networks with Probabilistic and Mixed Time-Varying Delays

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.

Synchronization Control of Memristive Multidirectional Associative Memory Neural Networks and Applications in Network Security Communication

In this paper, we investigate the synchronization in the mean square sense of memristive multidirectional associative memory neural networks with mixed time-varying delays and stochastic perturbations. In the proposed approach, the mixed delays include time-varying delays and distributed time delays. Sufficient criteria guaranteeing the synchronization of the drive-response system are derived based on the drive-response concept, the stochastic differential theory and Lyapunov function. With the removal of certain strict conditions of weight parameters, less conservative results are generated. To illustrate the performance of the proposed synchronization criteria, a secure communication scheme to realize secure data transmission is designed. Meanwhile, the effectiveness of the proposed theories is validated with numerical experiments.

Synchronization of a Class of Memristive Stochastic Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays via Sampled-Data Control

The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs) with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Exponential Stabilization of Coupled Hybrid Stochastic Delayed BAM Neural Networks: A Periodically Intermittent Control Method

This paper considers exponential stabilization for a class of coupled hybrid stochastic delayed bidirectional associative memory neural networks (HSD‐BAM‐NN) with reaction‐diffusion terms. A periodically intermittent controller is proposed to exponentially stabilize such an unstable HSD‐BAM‐NN, and sufficient conditions of the closed‐loop BAM‐NN system with exponential stabilization are derived by using Lyapunov‐Krasovskii functional method, stochastic analysis techniques, and integral inequality property, which decide the basic parameters of the proposed controller. Furthermore, a framework to establish simulation algorithm with sampled states is presented to implement the stabilization controller. With a HSD‐BAM‐NN model of power synchronization in a photovoltaic (PV) array field, we illustrate numerical simulation results to verify the correctness and effectiveness of the proposed controller.

Global Well-Posedness and Dynamical Behavior of Delayed Reaction-Diffusion BAM Neural Networks Driven by Wiener Processes

This paper studies the global existence and uniqueness as well as asymptotic behavior of the reaction-diffusion bidirectional associative memory neural networks with S-type distributed delays and infinite dimensional Wiener processes. The conspicuous characteristics of this system are neurons in one layer interacting with neurons in another layer and the noise which disturbed this system has both time and spatial structure. First, several inequalities are proposed and proved for the preparation of future study. Then, the system is coped in the framework of semigroup theory and functional space. Furthermore, the local existence and uniqueness of mild solution for this system is proven by using the contraction mapping principle coupled with many functional inequalities such as Young inequality, Burkholder–Davis–Gundy inequality, Poincare inequality. The global well-posedness are proven through a prior estimate from constructing appropriate Lyapunov–Krasovskii functional. Moreover, the existence of equilibrium is solved by using the topological degree theory and homotopy invariance. At last, the globally exponential stability of the equilibrium in the mean square sense is studied by constructing appropriate vector Lyapunov–Krasovskii functional and using an improved inequality proposed by us. The criteria of stability are given in the form of matrix form. It is easy to verify them in the computer and they will have a wider application. We give an example to examine the availability of our result, and the code is performed in Matlab. The approach used in this paper can also be extended to other systems.