Associative Memory Neural Network Model Research Articles

Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.

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.

New stability results for bidirectional associative memory neural networks model involving generalized piecewise constant delay

Bidirectional associative memories (BAMs) have been extensively applied in autoassociative and heteroassociative learning. However, the research on the implementation of BAM neural networks model with the effects of the constant delay is relatively few. The present work accumulates the global exponential stability criteria for the BAM neural networks model with deviation arguments. Here the effects of the constant delay of generalized type are provided, namely piecewise constant delay of generalized type (in short, DEGPCD). This article is principally concerned with the existence and global exponential stability of the BAM neural networks model with the DEGPCD system by using approach based on the construction of an equivalent integral equation. Applying the linearization method, Banach’s fixed point theorem, a DEGPCD integral inequality of Gronwall type and some inequality techniques, we establish a new sufficient condition to ensure the existence and global exponential stability of the equilibrium point of the BAM neural networks model with the DEGPCD system. The research indicates that the generalized piecewise constant delay has a vital effect on global exponential stability of the BAM neural networks model with the DEGPCD system. At the end of this work, the hypothesis has been established with two illustrative examples along with the simulations.

Global exponential stability of bidirectional associative memory neural networks model with piecewise alternately advanced and retarded argument

Global exponential stability of bidirectional associative memory neural networks model with piecewise alternately advanced and retarded argument

Asymptotic behavior of a BAM neural network with delays of distributed type

In this paper, we examine a Bidirectional Associative Memory neural network model with distributed delays. Using a result due to Cid [J. Math. Anal. Appl.281(2003) 264–275], we were able to prove an exponential stability result in the case when the standard Lipschitz continuity condition is violated. Indeed, we deal with activation functions which may not be Lipschitz continuous. Therefore, the standard Halanay inequality is not applicable. We will use a nonlinear version of this inequality. At the end, the obtained differential inequality which should imply the exponential stability appears ‘state dependent’. That is the usual constant depends in this case on the state itself. This adds some difficulties which we overcome by a suitable argument.

Bidirectional Spatio-Temporal Association Between the Observed Results of Ulva Prolifera Green Tides in the Yellow Sea and the Social Response in Sina Weibo

Massive green tides caused by Ulva prolifera have annually occurred in the Yellow Sea since 2007, which has attracted much attention from the government and society. There are associations between the green tides in the Yellow Sea and social response in the social media (i.e., Sina Weibo), which are bidirectional and could be captured by the bidirectional neural network. For instance, how to detect daily U. prolifera green tides by fusing remote sensing data with social media data, and how to use the observed U. prolifera green tides to infer the social response are two challenges of State Oceanic Administration, China. This article first illustrated that there are bidirectional associations between green tides and Sina Weibo data. Then, this article introduced a bidirectional spatio-temporal associative memory neural network (BSAMNN) model for modeling this bidirectional association from the spatio-temporal perspective. BSAMNN first extracted six characteristics from green tides and nine characteristics from the social responses in 2016-2019. Second, these characteristics were split by year, and the characteristics in 2016-2018 were, respectively, put into the bidirectional associative memory neural network (BAM), which is a two-layer artificial neural network. Based on the BAM results and the observed data, the residual network was constructed. Third, BSAMNN extracted the spatio-temporal rules from the characteristics in 2016-2018 as the constraints through the mining rule algorithm and modify the results via sea surface wind and ocean surface current. Last, BSAMNN put the characteristics in 2019 into BAM and used the residual network to modify the results, which was constrained by the spatio-temporal rules. The feasibility and reliability of our approach were demonstrated by using the U. prolifera green tides in 2019. The average accuracy, false alarm rate, and missing alarm rate of BSAMNN results were 0.69, 0.25, and 0.31, respectively, which was 0.11 higher, 0.10 lower, and 0.11 lower than that of the traditional BAM. The results indicated that our method is an effective alternative of linking the U. prolifera green tides and its public sentiments on social media.

Fixed-time synchronization of fractional order memristive MAM neural networks by sliding mode control

In this paper, we first established the fractional order memristive multidirectional associative memory neural networks (FMMAMNNs) model, and then considered its fixed-time synchronization control problem. On the basis of sliding model control and Lyapunov stability theorem, a fractional order sliding mode controller is constructed. By adding this controller to the response system, the error of the driver-response systems gradually converges to 0 in a fixed time. Compared with the previous researches, this paper considers a more complex model, and the proposed control theories can ensure that the setting time is only related to the model and controller, but not to the initial states of the system. Besides, the control theories are also applicable to the integer order models. Finally, two numerical simulations are given, the results show the validity of the theories.

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks.

In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.

Stability analysis of memristive multidirectional associative memory neural networks and applications in information storage

Traditional biological neural networks lack the capability of reflecting variable synaptic weights when simulating associative memory of human brains. In this paper, we investigate the existence and exponential stability of a novel memristive multidirectional associative memory neural networks (MAMNNs) model, which includes the time-varying delays. In the proposed approach, the time-varying delays are set to be bounded, and it is not necessary for their derivative to be differentiable. With removal of certain conditions, less conservative results are generated. Sufficient criteria guaranteeing the stability of the memristive MAMNNs are derived based on the Lyapunov function and some inequality techniques. To illustrate the performance of the proposed criteria, a procedure is designed to realize information storage. Meanwhile, the effectiveness of the proposed theories is validated with numerical experiments.

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.

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.

Bogdanov-Takens bifurcation in a neutral BAM neural networks model with delays.

In this study, the authors first discuss the existence of Bogdanov-Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second-order and the third-order normal forms of the Bogdanov-Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non-trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non-trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov-Takens bifurcation critical point.

Periodic Solutions of BAM Neural Networks with Continuously Distributed Delays in the Leakage Terms

This paper concerns with bidirectional associative memory neural network model with continuously distributed leakage delays. By applying Lyapunov functional method and differential inequality techniques, we establish some sufficient conditions for the existence and exponential stability of periodic solutions for the model, which complement with some recent ones. Moreover, an example and its numerical simulation are given to support the theoretical results.

Hopf bifurcation of an (n + 1) -neuron bidirectional associative memory neural network model with delays.

Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.

Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model

In this paper, a bidirectional associative memory (BAM) neural network model, which consists of two neurons in the X-layer and three neurons in the Y-layer, with two time delays, will be considered. By analyzing the associated characteristic equation, we obtain that Hopf bifurcation occurs and a family of periodic solutions appears. Moreover, the stability and the period of the bifurcating periodic solutions are studied. To illustrate our theoretical results, numerical simulations are presented.

Global Exponential Stability of Discrete-Time Multidirectional Associative Memory Neural Network with Variable Delays

A discrete-time multidirectional associative memory neural networks model with varying time delays is formulated by employing the semidiscretization method. A sufficient condition for the existence of an equilibrium point is given. By calculating difference and using inequality technique, a sufficient condition for the global exponential stability of the equilibrium point is obtained. The results are helpful to design global exponentially stable multidirectional associative memory neural networks. An example is given to illustrate the effectiveness of the results.

LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions

Abstract In this paper, the exponential stability analysis for the bidirectional associative memory neural network model with both time-varying delays and general activation functions is considered. Neither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functional and the linear matrix inequality (LMI) approach, several new sufficient conditions in LMI form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via an example with simulation.

Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks

Abstract In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23] . An example is provided to show the correctness of our analysis.

Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.

Periodic oscillation of discrete-time bidirectional associative memory neural networks

In this paper, a discrete-time bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we give some sufficient conditions ensuring the existence and globally exponential stability of periodic solutions for the discrete-time bidirectional neural networks. An example with the numerical simulations is provided to show the correctness of our analysis.