Search

A review of the basic Hansen's ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge. [ABSTRACT FROM AUTHOR]

Summary: In this article, the global and exponential synchronization of Lur'e networks with hybrid time‐varying delays is investigated. For sake of saving control costs, a novel impulsive adaptive controller is presented, where the adaptive feedback control input is utilized to compensate the control effects of the impulsive signal. Meanwhile, suitable control gains are obtained according to the designing on adaptive updating laws. In view of the definition of average impulsive interval, the generalized comparison principle and the formula of parameter variation, sufficient conditions for achieving global and exponential synchronization of Lur'e dynamical networks are eventually derived. Two relevant numerical simulations are provided to illustrate the effectiveness of theoretical analysis and the control scheme. [ABSTRACT FROM AUTHOR]

In this study, multiplicative conformable fractional differential equations are presented. Wronskian concept, linear dependence-independence concepts are defined on multiplicative conformable fractional calculus and some theorems and results are given among them. Finally, some examples are solved by giving some methods for finding general solutions of multiplicative conformable fractional differential equations. [ABSTRACT FROM AUTHOR]

Summary: This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time‐varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster‐tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples. [ABSTRACT FROM AUTHOR]

This article is devoted to study the cluster synchronization for a kind of complex dynamical networks consisting of nonidentical nonlinear Lur’e systems. Different from general time delays, a proportional delay is taken into consideration in this article, which is a kind of unbounded time-varying delays and thus largely increases the difficulty in network synchronization. In consideration of the topology structures of the Lur’e networks, an effective impulsive pinning controller is proposed, which will be placed on the Lur’e systems having directed paths with those in the other clusters. Considering different functional roles that the impulsive effects play, sufficient criteria for the cluster synchronization of the nonidentically coupled Lur’e dynamical networks are obtained by applying the proportionally delayed impulsive comparison principle, the concept of average impulsive interval, and the extended parameters variation formula. Simultaneously, the exponential convergence rates are successfully estimated with respect to different functions of the impulsive effects. In the end of this article, three numerical simulations are proposed to denote the effectiveness of the control protocols and the theoretical results. [ABSTRACT FROM AUTHOR]