Fractional-order Bidirectional Associative Memory Research Articles

Effect of Leakage Delays on Bifurcation in Fractional-Order Bidirectional Associative Memory Neural Networks with Five Neurons and Discrete Delays

Effect of Leakage Delays on Bifurcation in Fractional-Order Bidirectional Associative Memory Neural Networks with Five Neurons and Discrete 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.

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.

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.

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

带有比例时滞的分数阶双向联想记忆神经网络的有限时间稳定

带有比例时滞的分数阶双向联想记忆神经网络的有限时间稳定

Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays

This article aims to deal with the stability and Hopf bifurcation analysis for a type of fractional-order bidirectional associative memory (BAM) neural network involving two neurons in the X-layer and n neurons in the Y-layer, respectively. In view of the universal existence and multiplicity of time delay in many real systems, leakage delay and nonuniform communication delays are both taken into account. Coates’s flow-graph formula is efficiently adopted to solve the high-order characteristic equation of the associated linearized system. By making some assumptions on the mixed time delays, the obtained characteristic equation only contains the leakage delay, which is selected as the bifurcation parameter. Utilizing the discriminated criteria of stability for fractional-order dynamical systems and Hopf bifurcation theory, we obtain the critical value of the bifurcation point, greater than which the Hopf bifurcation would occur. Particularly, the stability and Hopf bifurcation is also analyzed for the case of no leakage delay to get an insight into the effect of the leakage delay. Finally, the validity of our theoretical results is substantiated through a simulation example.

New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays

• A novel generalized FODGI with two different orders is developed, which includes the one in [39, Theorem 3.2] as a special case and can be used to analyze the qualitative properties of various FODSs with two different orders. • As a straightforward generalization, a novel generalized FODGI with multiple different orders is also established, which includes the one in [40, Theorem 1.4] as a special case. • Two novel FTS criteria of FOBAMNNs with the orders 0 < ℘ < 1 and 1 < ℘< 2 are established by the obtained FODGI with two different orders. In this approach, the term w ( t ) and delay term w ( t − τ ) can be analyzed in a unified framework. This is to say, the delay term w ( t − τ ) needs not to be transformed to the term w ( t ). • Comparisons with the existing contributions: a) The obtained results in this article is less conservative than the ones in the existing works [30, 31]. b) There are delay terms in the obtained novel FODGI with multiple different orders. Therefore, the proposed inequality in this article is more general. The finite-time stability (FTS) for fractional-order bidirectional associative memory neural networks (FOBAMNNs) with discrete and distributed delays is investigated in this article. Firstly, a novel fractional-order delayed Gronwall inequality (FODGI) with two different orders is developed. As a straightforward generalization, a novel generalized FODGI with multiple different orders is also established, which can be applied to investigate the stability of fractional-order delayed systems (FODSs) with multiple different orders. Secondly, based on the former inequality, two novel FTS criteria of FOBAMNNs with the orders 0 < ℘ < 1 and 1 < ℘ < 2 are established. Finally, three examples are exhibited to illustrate the effectiveness and the less conservativeness of the proposed methods.

Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality

This paper is concerned with the problem of global synchronization for a class of uncertain fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with constant time delay. Some linear matrix inequality (LMI) based conditions have been established for ensuring the stability behavior of the governing augmented system derived from the considered fractional-order master system and the constructed slave system. In such LMI conditions, for utilizing the information on the time delay terms and the order of the fractional derivative, some fractional-order integral inequalities have been developed. Next, by defining a new Lyapunov–Krasovskii functional (LKF) and based on the improved fractional-order inequalities, the global synchronization criteria have been established in terms of a solvable set of LMIs for the considered class of uncertain FOBAM NNs without uncertain matrices. Further, the obtained results have been extended to the case of uncertain FOBAM NNs. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed theoretical results.

Bifurcations in a fractional-order BAM neural network with four different delays

This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.

DYNAMICS OF A FRACTIONAL-ORDER BAM NEURAL NETWORK WITH LEAKAGE DELAY AND COMMUNICATION DELAY

This paper lucubrates the bifurcations of a fractional-order bidirectional associative memory neural network (FOBAMNN) with leakage and communication delays. Firstly, leakage delay is taken as a bifurcation parameter to detect the bifurcations of the proposed neural network (NN). Leakage delay-induced bifurcation results are commendably established. Then communication delay is regarded as a bifurcation parameter to investigate the bifurcations of the developed FOBAMNN, and the stability interval and bifurcation point are derived. It reveals that the devised FOBAMNN possesses outstanding stability performance if selecting a lesser value of them, while the bifurcation emerges of FOBAMNN and eventually leads to performance deterioration with an outsize one. Besides, the influence of fractional order on the bifurcation points is carefully studied. It perceives that a proper fractional order can heighten the stability performance of the developed FOBAMNN. Ultimately, numerical simulations are exploited to underpin the developed theory.

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method.

Finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays

This paper investigates the finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The sufficient conditions are derived to ensure the finite-time stability of systems by employing some analytical techniques and some inequalities. In addition, some conditions are achieved to guarantee the existence, the uniqueness and the finite-time stability of equilibrium point. Finally, two numerical examples are given to verify the effectiveness of the obtained main results.

Robust state estimation for fractional-order delayed BAM neural networks via LMI approach

This paper is concerned with the robust state estimation problem for a class of delayed fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with norm-bounded uncertainties. The objective of the study is to construct an efficient estimator in such a way that the behavior of the corresponding error state is stable in the Mittag-Leffler sense. Distinct to the previous studies, the state estimation problem of FOBAM NNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global Mittag-Leffler stability of the error system are derived as a set of solvable linear matrix inequalities (LMIs) without uncertainties. The proposed stability conditions are further extended to the FOBAM NNs by considering the effect of uncertainties. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.

Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

Global stabilization of fractional-order bidirectional associative memory neural networks with mixed time delays via adaptive feedback control

This paper focuses on the stabilization problem for a class of fractional-order bidirectional associative memory neural networks with mixed time delays (discrete delay and finite-time distributed delay). Based on adaptive control and delay feedback control, two kinds of adaptive control schemes are proposed to realize the global stabilization of systems. Different from those in earlier works, our method mainly depends on two fractional inequalities and a new fractional-order Barbalat lemma. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed adaptive control schemes.

Global stabilization of a class of fractional-order delayed bidirectional associative memory neural networks

This paper focuses on the stabilization problem of a class of fractional-order bidirectional associative memory neural networks with time delays. Based on feedback control, a sufficient condition is derived to achieve the global stabilization of systems by using the fractional inequality, the Lyapunov stability theory, and the comparison principle. In particular, this kind of control scheme is proved to be robust in the presence of external disturbances when the feedback gains are sufficiently large. In addition, a condition is obtained to achieve the global quasi-stabilization of systems with some external disturbances, and the corresponding error bound is estimated. Finally, some numerical simulations are presented to verify the effectiveness of theoretical results.

Adaptive control of Mittag-Leffler stabilization and synchronization for delayed fractional-order BAM neural networks

This paper is committed to studying adaptive control design of Mittag-Leffler stabilization and synchronization for delayed fractional-order bidirectional associative memory (BAM) neural networks. Considering better dynamic property and steady state performance of the system, we adopt adaptive control approaches to stabilize and synchronize two types of delayed fractional-order BAM neural network. It is a remarkable fact, based on adaptive control scheme, the method of auxiliary functions, Mittag-Leffler stabilization and synchronization theories with respect to fractional-order systems, the adaptive controllers are very well designed in a controlled system and two coupled systems, separately. Two examples are performed to illustrate the advantage of the presented theoretic analysis and results.

Influence of Time Delay on Bifurcation in Fractional Order BAM Neural Networks With Four Delays

Over the past several decades, numerous scholars have studied the stability and Hopf bifurcation problem of integer-order delayed neural networks. However, the fruits about the stability and Hopf bifurcation for fractional-order delayed neural networks are very scarce. In this paper, we will consider the stability and the existence of Hopf bifurcation of fractional-order bidirectional associative memory (BAM) neural networks with four delays. A set of sufficient criteria to ensure the stability and the existence of Hopf bifurcation for the fractional-order BAM neural networks with four delays are established by choosing the sum of two different delays as a bifurcation parameter. This paper manifests that the delay has an important influence on the stability and Hopf bifurcation of involved networks. An example is displayed to test the rationality of the derived theoretical findings. The derived results of this paper are new and play a key role in optimizing networks and improving human life.