Multidirectional Associative Memory Neural Networks Research Articles

Finite-time multistability of a multidirectional associative memory neural network with multiple fractional orders based on a generalized Gronwall inequality

Finite-time multistability of a multidirectional associative memory neural network with multiple fractional orders based on a generalized Gronwall inequality

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.

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.

Almost periodic solutions of memristive multidirectional associative memory neural networks with mixed time delays

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains. In this paper, the memristive multidirectional associative memory neural networks (MAMNNs) with mixed time-varying delays are investigated in the sense of Filippov solution. First, three steps are given to prove the existence of the almost periodic solution. Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function. Second, the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function. The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions, Halanay inequality and Lyapunov function. The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks. Finally, numerical examples with simulations are presented to show the validity of the main results.

Master–slave synchronization of fractional-order memristive MAM neural networks with parameter disturbances and mixed delays

In order to describe the system as realistically as possible, the fractional-order memristive multidirectional associative memory neural networks (FOMMAMNNs) with parameter disturbances, time-varying and distributed delays are established. Further, the master–slave synchronization is explored. Firstly, in the Filippov’s sense, some conditions are derived via the contraction mapping principle to guarantee the uniqueness of equilibrium point of the system. Secondly, from the perspective of reducing control costs, pinning controller and adaptive pinning controller are designed for the first time to induce synchronization of FOMMAMNNs. Moreover, some synchronization criteria are obtained by using the properties of fractional calculus, the appropriate Lyapunov candidate functions and fractional Barbalat’s lemma. Thirdly, a communication scheme based on chaotic synchronization is proposed to achieve the safe transmission of important information. Finally, two numerical simulations are given to illustrate the feasibility of the theoretical results and the security of the designed communication scheme.

Projective synchronization of memristive multidirectional associative memory neural networks via self-triggered impulsive control and its application to image protection

This paper presents a new synchronization criterion with a hybrid control approach for multidirectional associative memory neural networks based on memristor (MMAMNNs). That is, the method of impulsive and feedback control combing with the (event) self-triggered mechanism is adopted. However some projective synchronization errors based on state related parameters of MMAMNNs will be affected by the diverse initial conditions. Thus, the new criterion is supported by establishing a novel Lyapunov function combined with the features of such diverse parameters and systems. A collaborative proposed method is designed to make the error of such system converging to zero. Then, the Zeno-behavior is testified to disappear from the proposed programs. Finally, some examples demonstrate the validity of the proposed method and to show its potential application in image protection.

Impulsive multidirectional associative memory neural networks: New results

An Impulsive Multidirectional Associative Memory Neural Network (IMAMNN) with time-varying and leakage delays is proposed. Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work. Moreover, two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.

Existence and exponential stability of almost-periodic solutions for MAM neural network with distributed delays on time scales

This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales. Some sufficient conditions on the existence, uniqueness and the global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results.

Global dissipativity of Clifford-valued multidirectional associative memory neural networks with mixed delays

The main goal of this article is to study the global dissipativity problem of Clifford-Valued Multidirectional Associative Memory Neural Networks (CVMAMNNs) with time-varying delays and distributed delays. Based on Lyapunov functionals and Linear Matrix Inequalities (LMIs) approach, new sufficient conditions are derived to ensure the global dissipativity and global exponential dissipativity of the considered network model. Moreover, the global attractive set and global exponential attractive set are obtained which are positive invariant ones. Finally, two numerical examples with simulations are given to illustrate the effectiveness of the analytical findings.

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.

Fixed-time synchronization control of memristive MAM neural networks with mixed delays and application in chaotic secure communication

Abstract In this paper, the fixed-time synchronization control problem of memristive multidirectional associative memory neural networks (MMAMNNs) is considered. Based on the nonlinear and chaos characteristics of memristor, a chaotic model is constructed. And then, utilizing the Lyapunov stability theory, two appropriate controllers are constructed and different activation functions are used. This control method ensures that drive system and response system can achieve synchronization within a fixed time. So, compared with previous studies, it has more practical value. In addition, we present a fixed-time synchronization chaotic encryption method, the chaos characteristic of the model is used to encrypt plaintext, and the decryption of ciphertext is realized based on the synchronization control theories. Finally, several numerical simulations are given to demonstrate the validity of the theories and the chaotic secure communication scheme.

Oscillation and stability of multidirectional associative memory neural network with mixed delays

This paper deals with a generalized multidirectional associative memory neural network with time-varying coefficients and mixed delays. Some criteria are established for the existence and the global exponential stability of weighted pseudo almost-periodic solutions for the studied model. To do so, the exponential dichotomy theory, the contraction mapping fixed point theorem and the differential inequality techniques are used. Moreover, an example and its numerical simulation are employed to illustrate the main results.

The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control.

In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.

Pseudo Almost Automorphic Solutions for Multidirectional Associative Memory Neural Network with Mixed Delays

In the paper, under some sufficient conditions, the existence and the global exponential stability of a pseudo almost automorphic solution to multidirectional associative memory (MAM) neural network with time-varying coefficients and mixed delays is obtained by combining both differential inequality techniques and the classical Banach’s fixed-point principle. As you will see, our results improve and generalize many previous known results in MAM. Finally, an example together with its numeric simulations show the feasibility and effectiveness of our main results.

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.

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.

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.

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.

Multiplicity of almost periodic solutions for multidirectional associative memory neural network with distributed delays

In this paper, the multiplicity of almost periodic solutions is studied for a multidirectional associative memory (MAM) neural network with almost periodic coefficients and continuously distributed delays. Under some assumptions on activation functions, some invariant subsets of the MAM neural network are constructed. The existence of multiple almost periodic solutions are obtained by using the theory of exponential dichotomy and Schauder׳s fixed point theorem. Furthermore, a sufficient condition is derived for the local exponential stability of some almost periodic solutions and their exponential attracting domains are also given. An example is given to illustrate the effectiveness of the results.