scholarly journals Dynamics Models of Synchronized Piecewise Linear Discrete Chaotic Systems of High Order

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 236 ◽  
Author(s):  
Sergei Sokolov ◽  
Anton Zhilenkov ◽  
Sergei Chernyi ◽  
Anatoliy Nyrkov ◽  
David Mamunts
Keyword(s):  
Dynamic Characteristics ◽  
Chaotic Systems ◽  
Phase Synchronization ◽  
Piecewise Linear ◽  
Discrete Systems ◽  
Third Order ◽  
The Third ◽  
Discrete Phase ◽  
Dynamics Models ◽  
Nonlinear Motions

This paper deals with the methods for investigating the nonlinear dynamics of discrete chaotic systems (DCS) applied to piecewise linear systems of the third order. The paper proposes an approach to the analysis of the systems under research and their improvement. Thus, effective and mathematically sound methods for the analysis of nonlinear motions in the models under consideration are proposed. It makes it possible to obtain simple calculated relations for determining the basic dynamic characteristics of systems. Based on these methods, the authors developed algorithms for calculating the dynamic characteristics of discrete systems, i.e. areas of the existence of steady-state motion, areas of stability, capture band, and parameters of transients. By virtue of the developed methods and algorithms, the dynamic modes of several models of discrete phase synchronization systems can be analyzed. They are as follows: Pulsed and digital different orders, dual-ring systems of various types, including combined ones, and systems with cyclic interruption of auto-tuning. The efficiency of various devices for information processing, generation and stabilization could be increased by using the mentioned discrete synchronization systems on the grounds of the results of the analysis. We are now developing original software for analyzing the dynamic characteristics of various classes of discrete phase synchronization systems, based on the developed methods and algorithms.

scholarly journals Adaptive smoothing approximation in the construction problem for hydrometeorological fields

2018 ◽  
pp. 449-463
Author(s):  
Б.Н. Иванов
Keyword(s):  
Least Squares Method ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Data Availability ◽  
Approximation Procedure ◽  
Third Order ◽  
Adaptive Smoothing ◽  
The Third ◽  
Universal Approach ◽  
Grid Nodes

Рассматривается процедура сглаживающей аппроксимации, которая позволяет адаптировать кусочно-линейную изолинию к ее представлению многочленами до третьего порядка. Сглаживающая аппроксимация уменьшает влияние ошибок линейной интерполяции при построении изолиний. В основе процедуры лежит метод наименьших квадратов. Выполнен анализ методов восполнения данных сплайновой кубической интерполяцией, наиболее часто используемых в практических работах. Рассматривается универсальный подход формирования границы области построения изолиний на основе наличия данных в узлах расчетной сетки. A smoothing approximation procedure that allows one to adapt a piecewise linear isoline to its representation by polynomials up to the third order is considered. The smoothing approximation reduces the effect of linear interpolation errors in isoline plotting. The procedure is based on the least-squares method. The data replenishment methods of spline cubic interpolation, most commonly used in practical work, are analyzed. A universal approach for the formation of boundaries of isoline areas on the basis of data availability at the computational grid nodes is discussed.

scholarly journals The approximated dynamic vehicle characteristics constructed based on the driving tests

2011 ◽  
Vol 146 (3) ◽  
pp. 38-44
Author(s):  
Kazimierz ROMANISZYN ◽  
Henryk WNĘK
Keyword(s):  
Fuel Consumption ◽  
Dynamic Characteristics ◽  
Exhaust Emissions ◽  
Third Order ◽  
The Third ◽  
Class C ◽  
The Individual ◽  
Engine Crankshaft ◽  
Combined Data

The paper presents the issue of the construction of the fuel consumption and exhaust emissions dynamic characteristics based on the data obtained during the NEDC and FTP-75 driving tests. The results presented in the publication are based on the tests of a class C vehicle, performed in a certified exhaust emissions laboratory. The distributions of engine crankshaft accelerations as a function of its speed for both tests at 1-second intervals have been collated. At these points the measurements of the exhaust emissions were carried out. The authors described the conditions in which modal measurements of the fuel consumption and exhaust emissions in both tests were carried out. The results of the measurements were used for the construction of the approximated characteristics being the functions of velocity and acceleration of the engine crankshaft. Based on the obtained measuring results the approximated dynamic characteristics of the emissions of the four main exhaust components have been developed and the approximations were done with the use of the third order functions. An analysis of the obtained results has been performed and the authors presented the differences resulting from the construction of the above characteristics based on the combined data from the NEDC and FTP-75 tests and each of the tests separately. Moreover, the differences between the data obtained from the individual tests have been presented and evaluated graphically. The obtained results have been summarized and evaluated.

scholarly journals SIMPLEST ODE EQUIVALENTS OF CHUA'S EQUATIONS

2000 ◽  
Vol 10 (01) ◽  
pp. 1-23 ◽  
Author(s):  
JIŘÍ POSPÍŠIL ◽  
ZDENĚK KOLKA ◽  
JANA HORSKÁ ◽  
JAROMÍR BRZOBOHATÝ
Keyword(s):  
Dynamical Systems ◽  
Piecewise Linear ◽  
Order System ◽  
Topological Conjugacy ◽  
Third Order ◽  
The Third ◽  
Canonical State ◽  
Stereoscopic View ◽  
State Models ◽  
Mutual Relations

The so-called elementary canonical state models of the third-order piecewise-linear (PWL) dynamical systems, as the simplest ODE equivalents of Chua's equations, are presented. Their mutual relations using the linear topological conjugacy are demonstrated in order to show in detail that Chua's equations and their canonical ODE equivalents represent various forms of qualitatively equivalent models of third-order dynamical systems. New geometrical aspects of the corresponding transformations together with examples of typical chaotic attractors in the stereoscopic view, give the possibility of a deeper insight into the third-order system dynamics.

Breathers and multiple rogue waves solutions of the (3+1)-dimensional Jimbo–Miwa equation

2021 ◽  
pp. 2150183
Author(s):  
Hong-Yi Zhang ◽  
Yu-Feng Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Hirota Bilinear

In this paper, we construct the breathers of the (3+1)-dimensional Jimbo–Miwa (JM) equation by means of the Hirota bilinear method, then based on the Hirota bilinear method with a new ansatz form, the multiple rogue wave solutions are constructed. Here, we discuss the general breathers, first-order rogue waves, the second-order rogue waves and the third-order rogue waves. Then we draw the 3- and 2-dimensional plots to illustrate the dynamic characteristics of breathers and multiple rogue waves. These interesting results will help us better reveal (3+1)-dimensional JM equation evolution mechanism.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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