Associative Memory Neural Networks Research Articles

Stability Analysis of Fractional Bidirectional Associative Memory Neural Networks With Multiple Proportional Delays and Distributed Delays.

This article investigates the finite-time stability of a class of fractional-order bidirectional associative memory neural networks (FOBAMNNs) with multiple proportional and distributed delays. Different from the existing Gronwall integral inequality with single proportional delay ( N = 1 ), we establish the Gronwall integral inequality with multiple proportional delays for the first time in the case of N ≥ 2 . Since the existing fractional-order single-constant delay Gronwall inequality with two different orders cannot be directly applied to the stability analysis of the aforementioned system, initially, we skillfully develop a novel one with generalized fractional multiproportional delays' Gronwall inequalities of different orders. Furthermore, combined with the newly constructed generalized inequality, the stability criteria of FOBAMNNs with fractional orders and under weaker conditions, i.e., at most linear growth and linear growth conditions rather than the global Lipschitz condition, are given respectively. Finally, numerical experiments verify the effectiveness of the proposed method.

A sampled-data stabilisation analysis on memristive BAM neural networks for memductance function

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results.

Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions

This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov–Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results.

Bifurcations of a delayed fractional-order BAM neural network via new parameter perturbations

This paper makes a new breakthrough in deliberating the bifurcations of fractional-order bidirectional associative memory neural network (FOBAMNN). In the beginning, the corresponding bifurcation results are established according to self-regulating parameter, which is different from bifurcation outcomes available by using time delay as the bifurcation parameter, and greatly enriches the bifurcation results of continuous neural networks(NNs). The deived results manifest that a larger self-regulating parameter is more conducive to the stability of the system, which is consistent with the actual meaning of the self-regulating parameter representing the decay rate of activity. In addition to the innovation in the research object, this paper also has innovation in the procedure of calculating the bifurcation critical point. In the face of the quartic equation about the bifurcation parameters, this paper utilizes the methodology of implicit array to calculate the bifurcation critical point succinctly and effectively, which eschews the disadvantages of the conventional Ferrari approach, such as cumbersome formula and huge computational efforts. Our developed technique can be employed as a general method to solve the bifurcation point including the problem of dealing with the bifurcation critical point of delay. Ultimately, numerical experiments test the key theoretical fruits of this paper.

Finite-Time Synchronization for Stochastic Fractional-Order Memristive BAM Neural Networks with Multiple Delays

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time

We are devoted, in this paper, to the study of the pre-assigned-time drive-response synchronization problem for a class of Takagi–Sugeno fuzzy logic-based stochastic bidirectional associative memory neural networks, driven by Brownian motion, with continuous-time delay and (finitely and infinitely) distributed time delay. To achieve the drive-response synchronization between the neural network systems, concerned in this paper, and the corresponding response neural network systems (identical to our concerned neural network systems), we bring forward, based on the structural properties, a class of control strategies. By meticulously coining an elaborate Lyapunov–Krasovskii functional, we prove a criterion guaranteeing the desired pre-assigned-time drive-response synchronizability: For any given positive time instant, some of our designed controls make sure that our concerned neural network systems and the corresponding response neural network systems achieve synchronization, with the settling times not exceeding the pre-assigned positive time instant. In addition, we equip our theoretical studies with a numerical example, to illustrate that the synchronization controls designed in this paper are indeed effective. Our concerned neural network systems incorporate several types of time delays simultaneously, in particular, they have a continuous-time delay in their leakage terms, are based on Takagi–Sugeno fuzzy logic, and can be synchronized before any pre-given finite-time instant by the suggested control; therefore, our theoretical results in this paper have wide potential applications in the real world. The conservatism is reduced by introducing parameters in our designed Lyapunov–Krasovskii functional and synchronization control.

A multilayered bidirectional associative memory model for learning nonlinear tasks

A multilayered bidirectional associative memory neural network is proposed to account for learning nonlinear types of association. The model (denoted as the MF-BAM) is composed of two modules, the Multi-Feature extracting bidirectional associative memory (MF), which contains various unsupervised network layers, and a modified Bidirectional Associative Memory (BAM), which consists of a single supervised network layer. The MF generates successive feature patterns from the original inputs. These patterns change the relationship between the inputs and targets in a way that the BAM can learn. The model was tested on different nonlinear tasks, such as the N-bit, Double Moon and its variants, and the 3-class spiral task. Behaviors were reported through learning errors, decision zones, and recall performances. Results showed that it was possible to learn all tasks consistently. By manipulating the number of units per layer and the number of unsupervised network layers in the MF, it was possible to change the level of nonlinearity observed in the decision boundaries. Furthermore, results indicated that different behaviors were achieved from the same set of inputs by using the different generated patterns. These findings are significant as they showed how a BAM-inspired model could solve nonlinear tasks in a more cognitively plausible fashion.

Bifurcation Analysis of a Fractional-Order Bidirectional Associative Memory Neural Network with Multiple Delays

Bifurcation Analysis of a Fractional-Order Bidirectional Associative Memory Neural Network with Multiple Delays

A novel fixed-time stability lemma and its application in the stability analysis of BAM neural networks.

In this paper, we put forward an interesting fixed-time (FXT) stability lemma, which is based on a whole new judging condition, and the minimum upper bound for the stability start time is obtained. In the new FXT stability lemma, the mathematical relation between the upper bound of the stability start time and the system parameters is very simple, and the judgment condition only involves two system parameters. To indicate the usability of the new FXT stability lemma, we utilize it to study the FXT stability of a bidirectional associative memory neural network (BAMNN) with bounded perturbations via sliding mode control. To match the developed FXT stability lemma, novel sliding mode state variables and a two-layer sliding mode controller are designed. According to the developed FXT stability lemma, the perturbed BAMNN can achieve FXT stability under the devised sliding mode controller. The upper bound of the stability start time can be calculated easily by virtue of the control parameters, and the sufficient conditions guaranteeing that the perturbed BAMNN can achieve FXT stability have also been derived. Last, we provide some confirmatory simulations.

Retracted: Empirical Analysis of Enterprise Financial Management Risk Prediction in View of Associative Memory Neural Network

Retracted: Empirical Analysis of Enterprise Financial Management Risk Prediction in View of Associative Memory Neural Network

Fixed-time stability of Cohen-Grossberg BAM neural networks with impulsive perturbations

This article concerns the problem of fixed-time stability (FXTS) of a Cohen-Grossberg bidirectional associative memory neural network (CGBAMNN) with destabilizing impulsive effects. A novel sufficient condition for the impulsive dynamical systems (IDSs) to be FXTS for destabilizing impulses is obtained. Different from the usual Lyapunov inequality for FXTS of IDSs, we have applied a new Lyapunov inequality to obtain the results under impulsive perturbations. Based on the average impulsive interval (AII) and the comparison principle, we have derived the results of this paper. Two types of continuous controllers: one with signum terms and another without signum terms, based on a new Lyapunov inequality, FXTS of CGBAMNN have been studied. The settling-time functions obtained in this article depend on the parameters of the impulsive sequences. Finally, two numerical examples, one is a cyber-physical system with deception attacks and another is a neural network, are given to validate the efficiency of our obtained theoretical results.

Periodic and Almost Periodic Solutions of Stochastic Inertial Bidirectional Associative Memory Neural Networks on Time Scales

The stochastic inertial bidirectional associative memory neural networks (SIBAMNNs) on time scales are considered in this paper, which can unify and generalize both continuous and discrete systems. It is of primary importance to derive the criteria for the existence and uniqueness of both periodic and almost periodic solutions of SIBAMNNs on time scales. Based on that, the criteria for their exponential stability on time scales are studied. Meanwhile, the effectiveness of all proposed criteria is demonstrated by numerical simulation. The above study proposes a new way to unify and generalize both continuous and discrete SIBAMNNs systems, and is applicable to some other practical neural network systems on time scales.

Multidirectional Associative Memory Neural Network Circuit Based on Memristor.

Multidirectional associative memory neural network(MAMNN) is a direct extension of bidirectional associative memory neural network, which can handle multiple associations. In this work, a circuit of MAMNN based on memristor is proposed, which simulates the complex associative memory behavior more in line with the brain mechanism. Firstly, the basic associative memory circuit is designed, which is mainly composed of memristive weight matrix circuit, adder module and activation circuit. It realizes the associative memory function of single-layer neurons input and single-layer neurons output, so that the information can be transmitted unidirectionally between double-layer neurons. Secondly, on this basis, an associative memory circuit with multi-layer neurons input and single-layer neurons output is realized, which makes information transfer unidirectionally between multi-layer neurons. Finally, several identical circuit architectures are extended, and they are combined into a MAMNN circuit through the feedback connection from the output to the input, which realizes the bidirectional transmission of information between multi-layer neurons. Pspice simulation shows that: 1) When single-layer neurons are selected to input data, the circuit can associate data from other multi-layer neurons, realizing one-to-many associative memory function in the brain. 2) When multi-layer neurons are selected to input data, the circuit can associate the target data and realize the many-to-one associative memory function in the brain. The MAMNN circuit is applied to the field of image processing, which can associate and restore damaged binary images, showing strong robustness.

Using Bidirectional Associative Memory Neural Networks to Solve the N-bit Task

Nowadays, artificial neural networks can easily solve the N-bit parity problem. However, each time a different level must be learned, the network must be retrained. This, combined with the exponential increase of learning trials required as N grows, make these models too different from how their biological counterpart solves them. This is because humans learn to recognize patterns, count, and determine if numbers are odd or even. Once they have learned these tasks, they can have them interact to solve any level without further training. This behavior is akin to performing multiple associations of different tasks. Therefore, it is proposed that by using bidirectional associative memory neural networks, it would be possible to solve the N-bit parity problem in a similar fashion to humans. To achieve this, two networks interacted; one served as a task Identifier and the other as a memory Extractor, giving the desired behavior influenced by the Identifier. Results showed that the model could solve the 2- to 9-bit in linear time once the associations were learned. Moreover, this was possible with 97% fewer inputs and no retraining. In addition, because of the recurrent nature of the model, it could also solve the tasks even under high noise levels.

Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

Applying delayed dynamical models to characterize the dynamics of neural networks has attracted great interest from scientific community. In this current manuscript, a kind of new tri‐neuron bidirectional associative memory (BAM) neural networks including delay are formulated. The properties of solution and Hopf bifurcation issue of the established tri‐neuron BAM neural networks including delay are investigated. First, we check the existence and uniqueness of the solution to the formulated delayed tri‐neuron BAM neural networks by virtue of fixed point theorem. Second, we seek the boundedness of the solution of the formulated delayed tri‐neuron BAM neural networks in view of a suitable function and inequality skills. Third, the delay‐independent criteria on stability and bifurcation of the formulated delayed tri‐neuron BAM neural networks are acquired. Fourth, Hopf bifurcation control aspect of the formulated delayed tri‐neuron BAM neural networks is explored via designing two proper hybrid controllers. To prove the accuracy of gained primary assertions, software simulation experiments are put into practice.

Memristor-Based Neural Network Circuit With Multimode Generalization and Differentiation on Pavlov Associative Memory

Most of the classical conditioning laws implemented by existing circuits are involved in learning and forgetting between only three neurons, and the problems between multiple neurons are not considered. In this article, a multimode generalization and differentiation circuit for the Pavlov associative memory is proposed based on memristors. The designed circuit is mainly composed of voltage control modules, synaptic neuron modules, and inhibition modules. The secondary differentiation is accomplished through the process of associative learning and forgetting among multiple neurons. The process of multiple generalization and differentiation is realized based on the nonvolatility and thresholding properties of memristors. The extinction inhibition and differentiation inhibition in forgetting is considered through the inhibition modules. The Pavlov associative memory neural network with multimodal generalization and differentiation may provide a reference for the further development of brain-like intelligence.

A novel fixed-time stability result and its application to synchronization of delayed multidirectional associative memory neural networks with discontinuous activations

In this paper, in order to realize time-saving and low-consumption secure communication based on fixed-time (FXT) synchronization, some new FXT stability results and a smaller upper bound of settling time are obtained by using inequality techniques, variable substitution method and some special functions, including beta function and incomplete beta function. Moreover, the FXT synchronization of delayed multidirectional associative memory (MAM) neural networks with discontinuous activations is investigated by employing the differential inclusion theory, the improved FXT stability theorem and a simple delay-independent nonlinear controller. Finally, a numerical simulation is given to verify the correctness of the theoretical results and the effectiveness of FXT synchronization in secure communication. The results show that the upper bound estimation of settling time in this paper is indeed smaller than that in some previous researches. In addition, the encrypted signals can be quickly decrypted based on the improved FXT stability results, but may not be decrypted by the existing FXT stability results.

Interacting dreaming neural networks

We study the interaction of agents, where each one consists of an associative memory neural network trained with the same memory patterns and possibly different reinforcement-unlearning dreaming periods. Using replica methods, we obtain the rich equilibrium phase diagram of the coupled agents. It shows phases such as the student–professor phase, where only one network benefits from the interaction while the other is unaffected; a mutualism phase, where both benefit; an indifferent phase and an insufficient phase, where neither are benefited nor impaired; a phase of amensalism where one is unchanged and the other is damaged. In addition to the paramagnetic and spin glass phases, there is also one we call the reinforced delusion phase, where agents concur without having finite overlaps with memory patterns. For zero coupling constant, the model becomes the reinforcement and removal dreaming model, which without dreaming is the Hopfield model. For finite coupling and a single memory pattern, it becomes a Mattis version of the Ashkin–Teller model.

Stability and hopf bifurcation of fractional complex–valued BAM neural networks with multiple time delays

In this paper dynamical behaviors of a class of high–order fractional complex–valued bidirectional associative memory neural networks with multiple time delays are investigated. Firstly, they are reduced to real–valued systems by separating the real and imaginary parts. Then, stability criteria of fractional complex–valued bidirectional associative memory neural networks without delay are obtained. Concerning the delay case, the time delay is set as a bifurcation parameter and the condition of Hopf bifurcation is given by analyzing roots of characteristic equations. Finally, two numerical examples are presented and illustrate that Hopf bifurcation does happen when time delay exceeds the critical value.