Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

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

A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results

Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

This paper addresses Master-Slave synchronization for some memristor- based fractional-order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional-order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann-Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set-valued map, differential inclusions theory, fractional Barbalat’s lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.This work was jointly supported with the financial support of RUSA - Phase 2.0 grant sanctioned vide letter No. F.24-51/2014-U (TNMulti-Gen), Dept.of Education Govt. of India, Thailand research grant fund (RSA5980019), the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002

Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays

This paper deals with the extended design of Mittag-Leffler state estimator and adaptive synchronization for fractional order BAM neural networks (FBNNs) with time delays. By the aid of Lyapunov direct approach and Razumikhin-type method a suitable fractional order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag-Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag-Leffler adaptive synchronization by means of some fractional order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.N/

Global Mittag-Leffler stability of Caputo fractional-order fuzzy inertial neural networks with delay

This paper deals with the global Mittag-Leffler stability (GMLS) of Caputo fractional-order fuzzy inertial neural networks with time delay (CFOFINND). Based on Lyapunov stability theory and global fractional Halanay inequalities, the existence of unique equilibrium point and GMLS of CFOFINND have been established. A numerical example is given to illustrate the effectiveness of our results

Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results

Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays

This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes

Synchronization analysis of coupled fractional-order neural networks with time-varying delays

In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems