Bidirectional Associative Memory Neural Networks Research Articles

Secure adaptive event-triggered anti-synchronization for BAM neural networks with energy-limited DoS attacks

This article focuses on the problem of adaptive event-triggered anti-synchronization control for bidirectional associative memory neural networks subject to energy-limited denial of service attacks. First, a novel adaptive event-triggered scheme is developed by resorting to the acknowledgment character technique, which can help conserve valuable communication resources and has better performance in resisting malicious cyber attacks compared to traditional schemes. Second, a more general attack strategy for denial of service attacks is proposed with the consideration of energy constraints, and an anti-synchronization error system is established to analyze the anti-synchronization behavior. Then, sufficient conditions are provided to guarantee the anti-synchronization of drive and response bidirectional associative memory neural networks in H∞ sense. Next, a design approach is obtained based on the above conditions for the controller gains. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed method and its superiority over the traditional event-triggered scheme.

Non-separation Method-Based Global Stability Criteria for Takagi–Sugeno Fuzzy Quaternion-Valued BAM Delayed Neural Networks Using Quaternion-valued Auxiliary Function-Based Integral Inequality

This paper focuses on the global asymptotic stability (GAS) problem for Takagi–Sugeno (T-S) fuzzy quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with discrete, distributed and leakage delays by using non-separation method. By applying T-S fuzzy model, we first consider a general form of T-S fuzzy QVBAMNNs with time delays. Then, by constructing appropriate Lyapunov–Krasovskii functionals and employing quaternion-valued integral inequalities and homeomorphism theory, several delay-dependent sufficient conditions are obtained to guarantee the existence and GAS of the considered neural networks (NNs). In addition, these theoretical results are presented in the form of quaternion-valued linear matrix inequalities (LMIs), which can be verified numerically using the effective YALMIP toolbox in MATLAB. Finally, two numerical illustrations are presented along with their simulations to demonstrate the validity of the theoretical analysis.

New Insights on Bidirectional Associative Memory Neural Networks with Leakage Delay Components and Time-Varying Delays Using Sampled-Data Control

The sampling data control of bidirectional associative memory (BAM) neural network with leakage delay is considered in this article. The BAM model is viewed as a mixed delay that combines a distributed delay, a discrete delay that varies over time, and a delay in the leaking period. The sampling system is then converted to a continuous time-delay system using an input delay method. In order to get adequate conditions in the form of linear matrix inequalities(LMIs), we build a new Lyapunov-Krasovskii Functional (LKF) in conjunction with the free weight matrix approach. Finally, a simulation results are given to show the efficiency of the theoretical approach.

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

In this paper, the global exponential stability of quaternion BAM neural networks with mixed delays is investigated. The involved delays include multiple time‐varying transmission delays and unbounded distributed delays. Existence and uniqueness of equilibrium point of the considered neural networks are investigated by using the homeomorphism theory between topology spaces. To show sufficient conditions for global exponential stability of the unique equilibrium point, a method based on estimation of solutions is presented. The acquired stability conditions contain only several simple linear scalar inequalities, which can be easily solved. The availability of theoretical results is shown by a numerical example. A point worth emphasizing is that the method based on estimation of solutions is applicable for models of many time‐delay systems after a minor modification.

Bifurcation Analysis of Time-Delayed Non-Commensurate Caputo Fractional Bi-Directional Associative Memory Neural Networks Composed of Three Neurons

We are concerned in this paper with the stability and bifurcation problems for three-neuron-based bi-directional associative memory neural networks that are involved with time delays in transmission terms and possess Caputo fractional derivatives of non-commensurate orders. For the fractional bi-directional associative memory neural networks that are dealt with in this paper, we view the time delays as the bifurcation parameters. Via a standard contraction mapping argument, we establish the existence and uniqueness of the state trajectories of the investigated fractional bi-directional associative memory neural networks. By utilizing the idea and technique of linearization, we analyze the influence of time delays on the dynamical behavior of the investigated neural networks, as well as establish and prove several stability/bifurcation criteria for the neural networks dealt with in this paper. According to each of our established criteria, the equilibrium states of the investigated fractional bi-directional associative memory neural networks are asymptotically stable when some of the time delays are less than strictly specific positive constants, i.e., when the thresholds or the bifurcation points undergo Hopf bifurcation in the concerned networks at the aforementioned threshold constants. In the meantime, we provide several illustrative examples to numerically and visually validate our stability and bifurcation results. Our stability and bifurcation theoretical results in this paper yield some insights into the cause mechanism of the bifurcation phenomena for some other complex phenomena, and this is extremely helpful for the design of feedback control to attenuate or even to remove such complex phenomena in the dynamics of fractional bi-directional associative memory neural networks with time delays.

Exploration on bifurcation for an incommensurate five-neuron fractional-order BAM neural network involving multiple delays

Some qualitative analyses of bifurcations for an incommensurate fractional-order neural network with delays are considered. At first, we display an incommensurate five-neuron fractional-order bidirectional associative memory neural network (FOBAMNN) with four delays. Next, the existence and uniqueness of the solution are analyzed. Afterward, from the perspective of the two different cases of delays inducing bifurcations, some sufficient criteria of the stability and the occurrence of Hopf bifurcation are established. Some numerical simulations are designed to verify the feasibility and validity of the obtained theorems. In addition, the effects of the delays on the stability and bifurcation of the integer-order neural network and the fractional-order neural network are discussed and some meaningful results are presented in the end.

Delay-independent control for synchronization of memristor-based BAM neural networks with parameter perturbation and strong mismatch via finite-time technology

This paper mainly studies the synchronization problem of memristor-based bidirectional associative memory neural networks (MBAMNNs) via finite-time technology. Different from the existing neural network dynamic models, the given model in this paper is focused on the impact of parameter perturbation and strong mismatch, where strong mismatch includes parameter mismatch and time-varying delay mismatch. These characteristics can make the model be closer to the actual situation. A delay-independent feedback control scheme, which can stabilize the error system within finite-time regardless of whether the past state is known or not, is designed. It is worth noting that the constant is replaced by a function with the exponential term in the delay-independent controller, which can save the control cost to a certain extent. Based on the integral inequality technique, some sufficient conditions for MBAMNNs to converge to the equilibrium point within finite-time are provided. The validity and correctness of the theoretical results are finally confirmed by numerical simulation.

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.

New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption

<abstract> <p>With the popularization of digital image technology, image information has inevitably developed to involved the disclosure of personal privacy; in this study, a color image encryption algorithm was designed to encrypt and decrypt images by using chaotic sequences of a class of memristor-based hybrid delayed bidirectional associative memory neural networks (MHDBAMNNs) to protect images from illegal acquisition and use. Additionally, the discontinuity problem of the right-hand side of the Filippov system due to the hopping property of the memristor has been treated by using differential inclusion and set-valued mapping theories, and a sufficient criterion for guaranteeing the synchronization of finite-time projections derived based on the drive-response concept, Lyppunov stability theorem, and inequality technique. To improve the security performance, a color image encryption algorithm based on a combination of Chen's hyperchaotic system and a DNA codec operation was adopted, also, the robustness and validity of our proposed approach was demonstrated through image performance analysis. Furthermore, the potential application of the model in secure transmission has been explored.</p> </abstract>

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.

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.