[PDF] Chaos Synchronization And Structures In Dynamics Of Systems With Cylindrical Phase Space eBook

Author : Nikolai Verichev
Publisher : Springer Nature
Page : 197 pages
File Size : 13,35 MB
Release : 2020-01-01
Category : Science
ISBN : 3030361039

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This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.

Author : Holm Altenbach
Publisher : Springer Nature
Page : 473 pages
File Size : 22,37 MB
Release : 2020-04-22
Category : Technology & Engineering
ISBN : 3030387089

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This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Author : Nikolai Verichev
Publisher : Cambridge Scholars Publishing
Page : 496 pages
File Size : 38,35 MB
Release : 2021-07-27
Category : Technology & Engineering
ISBN : 1527572978

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The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.

Author : Elhadj Zeraoulia
Publisher : World Scientific
Page : 268 pages
File Size : 24,60 MB
Release : 2011
Category : Science
ISBN : 9814340693

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This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

Author : Santo Banerjee
Publisher : Springer
Page : 297 pages
File Size : 16,18 MB
Release : 2013-06-12
Category : Science
ISBN : 3642340172

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Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

Author : Jesus M Gonzalez-miranda
Publisher : World Scientific
Page : 225 pages
File Size : 36,16 MB
Release : 2004-10-12
Category : Science
ISBN : 1783260556

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This book presents a comprehensive overview of the research and latest developments in the field of the dynamics of coupled and driven chaotic oscillators, aimed at a wide audience. Since 1990, there has been very active research devoted to the field, culminating in a considerable body of knowledge, while active research continues.The results presented in the book will be valuable for scientific analysis and explanation in various different scientific disciplines, with potential applications in medicine and engineering. The contents include a selection of the most basic theoretical results, as well as experiments and applications presented at a mathematical level suited to readers working in non-hard sciences. It will also be of interest to physicists and mathematicians looking for an introduction to the field./a

Author : Valery V Matrosov
Publisher : World Scientific
Page : 255 pages
File Size : 10,69 MB
Release : 2018-08-29
Category : Science
ISBN : 9813271965

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Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and ensembles, formed by interacting dynamical elements.Unfortunately, the applicability of analytical and qualitative methods of nonlinear dynamics to such complex systems is severely restricted due to the high dimension of phase space. Therefore, studying the simplest models of networks, which are ensembles with a small number of elements, becomes of particular interest. Such models allow to make use of the entire spectrum of analytical, qualitative, and numerical methods of nonlinear dynamics. This book is devoted to the investigation of a kind of such systems, namely small ensembles of coupled, phase-controlled oscillators. Both traditional issues, like synchronization, that are relevant for applications in radio-communications, radio-location, energy, etc., and nontraditional issues of excitation of chaotic oscillations and their possible application in advanced communication systems are addressed.

Author : Vadim Semenovich Anishchenko
Publisher : World Scientific
Page : 410 pages
File Size : 27,56 MB
Release : 1995
Category : Science
ISBN : 9789810221423

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In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.

Author : Sergey P. Kuznetsov
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 32,40 MB
Release : 2012-03-20
Category : Science
ISBN : 3642236669

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"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.

Author : Jordan Fleming Blocher
Publisher :
Page : 144 pages
File Size : 26,69 MB
Release : 2016
Category : Electronic books
ISBN :

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We study the synchronization of chaotic systems when the coupling between them contains both time averages and stochastic noise. Our model dynamics are given by the Lorenz equations which are a system of three ordinary differential equations in the variables X, Y and Z. Our theoretical results show that coupling two copies of the Lorenz equations using a feedback control which consists of time averages of the X variable leads to exact synchronization provided the time-averaging window is known and sufficiently small. In the presence of noise the convergence is to within a factor of the variance of the noise. The novelty of our investigation hinges on the analysis of the time averages. We also consider the case when the time-averaging window is not known and show that it is possible to tune the feedback control to recover the size of the time-averaging window. Further numerical computations show that synchronization is more accurate and occurs under much less stringent conditions than our theory requires.