Synchronization of clocks

Peer reviewedPostprin

Estimation of the largest Lyapunov exponent in systems with impacts

Abstract The method of estimation of the largest Lyapunov exponent for mechanical systems with impacts using the properties of synchronization phenomenon is demonstrated. The presented method is based on the coupling of two identical dynamical systems and is tested on the classical Dung oscillator with impacts.

Alternative Methods of the Largest Lyapunov Exponent Estimation with Applications to the Stability Analyses Based on the Dynamical Maps—Introduction to the Method

Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied invariants characterizing systems’ stability are Lyapunov exponents (LE). When information about the stability of a system is demanded, it can be determined based on the value of the largest Lyapunov exponent (LLE). Recently, we have shown that LLE can be estimated from the vector field properties by means of the most basic mathematical operations. The present article introduces new methods of LLE estimation for continuous systems and maps. We have shown that application of our approaches will introduce significant improvement of the efficiency. We have also proved that our approach is simpler and more efficient than commonly applied algorithms. Moreover, as our approach works in the case of dynamical maps, it also enables an easy application of this method in noncontinuous systems. We show comparisons of efficiencies of algorithms based our approach. In the last paragraph, we discuss a possibility of the estimation of LLE from maps and for noncontinuous systems and present results of our initial investigations

Percentage of Myeloid Dendritic Cells in Peripheral Venous Blood Is Negatively Related to Incidence of Graves’ Orbitopathy

The aim of the study was to evaluate the distribution of blood dendritic cells (DCs) in patients with Graves’ orbitopathy (GO) and to assess the influence of methylprednisolone therapy on subsets of peripheral blood mononuclear cells (PBMCs). Peripheral blood DC subsets were analyzed by flow cytometry in patients with active GO (n=17), inactive GO (n=8), and Graves’ disease (GD) without GO (n=8) and controls (n=15); additionally, in patients with active GO (n=17), analyses were done at three time points, i.e., before methylprednisolone treatment and after 6 weeks and after 12 weeks of the treatment. Percentage of myeloid DCs (mDCs) in PBMC fraction was significantly lower in patients with both active and inactive GO, compared to patients with GD without GO and controls (p0.05). In the present study, we have succeeded to firstly demonstrate—according to our knowledge—that blood mDCs are negatively related to GO incidence