Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks

Modern synergetic neural network for imbalanced small data classification

Deep learning's performance on the imbalanced small data is substantially degraded by overfitting. Recurrent neural networks retain better performance in such tasks by constructing dynamical systems for robustness. Synergetic neural network (SNN), a synergetic-based recurrent neural network, has superiorities in eliminating recall errors and pseudo memories, but is subject to frequent association errors. Since the cause remains unclear, most subsequent studies use genetic algorithms to adjust parameters for better accuracy, which occupies the parameter optimization space and hinders task-oriented tuning. To solve the problem and promote SNN's application capability, we propose the modern synergetic neural network (MSNN) model. MSNN solves the association error by correcting the state initialization method in the working process, liberating the parameter optimization space. In addition, MSNN optimizes the attention parameter of the network with the error backpropagation algorithm and the gradient bypass technique to allow the network to be trained jointly with other network layers. The self-learning of the attention parameter empowers the adaptation to the imbalanced sample size, further improving the classification performance. In 75 classification tasks of small UC Irvine Machine Learning Datasets, the average rank of the MSNN achieves the best result compared to 187 neural and non-neural network machine learning methods.

Modern Synergetic Neural Network for Synthetic Aperture Radar Target Recognition

Feature extraction is an important process for the automatic recognition of synthetic aperture radar targets, but the rising complexity of the recognition network means that the features are abstractly implied in the network parameters and the performances are difficult to attribute. We propose the modern synergetic neural network (MSNN), which transforms the feature extraction process into the prototype self-learning process by the deep fusion of an autoencoder (AE) and a synergetic neural network. We prove that nonlinear AEs (e.g., stacked and convolutional AE) with ReLU activation functions reach the global minimum when their weights can be divided into tuples of M-P inverses. Therefore, MSNN can use the AE training process as a novel and effective nonlinear prototypes self-learning module. In addition, MSNN improves learning efficiency and performance stability by making the codes spontaneously converge to one-hots with the dynamics of Synergetics instead of loss function manipulation. Experiments on the MSTAR dataset show that MSNN achieves state-of-the-art recognition accuracy. The feature visualization results show that the excellent performance of MSNN stems from the prototype learning to capture features that are not covered in the dataset. These representative prototypes ensure the accurate recognition of new samples.

Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays

This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave-convex activation functions. And then, the multiple μ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag-Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results.

Artificial neural networks: a practical review of applications involving fractional calculus

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

Novel methods to global Mittag-Leffler stability of delayed fractional-order quaternion-valued neural networks

In this paper, a type of fractional-order quaternion-valued neural networks (FOQVNNs) with leakage and time-varying delays is established to simulate real-world situations, and the global Mittag-Leffler stability of the system is investigated by using the non-decomposition method. First, to avoid decomposing the system into two complex-valued systems or four real-valued systems, a new sign function for quaternion numbers is introduced based on the ones for real and complex numbers. And two novel lemmas for quaternion-valued sign function and Caputo fractional derivative are established in quaternion domain, which are used to investigate the stability of FOQVNNs. Second, a concise and flexible quaternion-valued state feedback controller is directly designed and a novel 1-norm Lyapunov function composed of the absolute values of real and imaginary parts is established. Then, based on the designed quaternion-valued state feedback controller and the proposed lemmas, some sufficient conditions are given to ensure the global Mittag-Leffler stability of the system. Finally, a numerical simulation is given to verify the theoretical results.

Finite-time synchronization of fractional-order gene regulatory networks with time delay

As multi-gene networks transmit signals and products by synchronous cooperation, investigating the synchronization of gene regulatory networks may help us to explore the biological rhythm and internal mechanisms at molecular and cellular levels. We aim to induce a type of fractional-order gene regulatory networks to synchronize at finite-time point by designing feedback controls. Firstly, a unique equilibrium point of the network is proved by applying the principle of contraction mapping. Secondly, some sufficient conditions for finite-time synchronization of fractional-order gene regulatory networks with time delay are explored based on two kinds of different control techniques and fractional Lyapunov function approach, and the corresponding setting time is estimated. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.

Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results.

Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes

This paper is concerned with the drive-response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

Global [Formula: see text] stabilization of fractional-order memristive neural networks with time delays

This article is concerned with the global [Formula: see text] stabilization for a class of fractional-order memristive neural networks with time delays (FMDNNs). Two kinds of control scheme (i.e., state feedback control law and output feedback control law) are employed to stabilize a class of FMDNNs. Several stabilization conditions in form of algebraic criteria are presented based on a new fractional-order Lyapunov function method and Leibniz rule. Some examples are given to substantiate the effectiveness of the presented theoretical results.