Xujun Yang

Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay

Quasi-uniform synchronization of delayed fractional-order memristor-based neural networks (FMNNs) is discussed in this paper. On the basis of the theory of fractional differential equations and the theory of differential inclusion, the synchronization error system between the concerned drive system and the associated response system is formulated, and then, by employing Hlder inequality, Cp inequality and Gronwall-Bellman inequality, several sufficient criteria are proposed to ensure the quasi-uniform synchronization for the considered delayed FMNNs. Three simulation examples are also presented to illustrate the availability and correctness of the theoretical results.

Stability analysis of nonlinear fractional-order systems with variable-time impulses

This paper aims at analyzing the stability analysis for a class of variable-time impulsive fractional-order nonlinear systems. Based on the theory of fractional calculus, the theory of impulsive differential equation, inequality techniques, and the B-equivalence method, the variable-time jump operator of the considered system can be updated as a fixed-time substitution, and the fractional-order system with the latter operator can be regarded as the comparison system of the original system. In addition, both graphic illustration and theoretical explanation are presented. Finally, two numerical examples are shown to demonstrate the validity and feasibility of the obtained results.

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons

This paper talks about the stability and synchronization problems of fractional-order quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of M-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive-response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results.

Global Mittag–Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control

Abstract Global Mittag–Leffler projective synchronization for nonidentical delayed fractional-order neural networks based on the technique of delayed sliding mode control is addressed in this paper. Firstly, a delayed fractional-order integral sliding surface is constructed. Then, based on the theory of sliding mode control, a delayed sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, based on the fractional Lyapunov direct method and Razumikhin technique, states are converged to the prescribed sliding surface to carry out sliding motion, and some sufficient conditions are derived to realize global Mittag–Leffler projective synchronization of the addressed model. Secondly, as two special cases, complete synchronization and anti-synchronization of the addressed model are investigated. Finally, numerical simulations are presented to illustrate the feasibility and effectiveness of the achieved results.

Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks Via Impulsive Control

This paper aims at analyzing the impulsive synchronization of fractional-order neural works. Firstly, in view of control theory, by constructing a suitable impulsive response system with the designed controller, the synchronization error system between the drive system and the corresponding response system is given. Afterwards, based on the theory of impulsive differential equation, the theory of fractional differential equation, Lyapunov direct method, and inequality techniques, some effective sufficient criteria are established to guarantee the global Mittag-Leffler stability for the synchronization error system. Finally, several simulation examples are designed to demonstrate the effectiveness and feasibility of the obtained results.

Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects

Abstract In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat’s lemma, Riemann–Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results.