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

Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations

This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differ- ential inclusion theoretical analysis, the global existence of Filippov solution for FCGNNDDs is studied by means of the given growth condition. Second, by virtue of suitable Lyapunov functional, Young inequality and comparison theorem for fractional order delayed linear system, some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations. Third, the global asymptotic synchronization condition for FCGNNDDs is obtained based on the pinning control. At last, two numerical simula- tions are given to verify the theoretical findings.N/

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

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper

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

Global exponential stability conditions for quaternion-valued neural networks with leakage, transmission and distribution delays

This paper studies the global exponential stability problem of quaternion-valued neural networks (QVNNs) with leakage, transmission, and distribution delays. To address this issue, a direct method based on system solutions is proposed to ensure the global exponential stability of the considered network models. In addition, this method does not need to construct any Lyapunov-Krasovskii functional, which greatly reduces the amount of computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described