Quasi Conservative Systems Cycles Resonances And Chaos

Author : Albert D. Morozov
Publisher : World Scientific
Page : 342 pages
File Size : 55,7 Mb
Release : 1998
Category : Science
ISBN : 9810228104

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QUASI-conservative Systems by Albert D. Morozov Pdf

This monograph presents the theory of nonconservative systems close to nonlinear integrable ones. With the example of concrete quasi-conservative systems close to nonintegrable ones, the results of numerical analysis are given, and the problem of applying the small parameter method is analyzed.The fundamantal part of the book deals with the investigation of the perturbable systems. Both autonomous and nonautonomous (periodic in time) systems are considered. The global analysis of systems close to the two-dimensional Hamiltonian ones takes a central place in the text. This global analysis includes the solution to problems such as the limit cycles, resonances, and nonregular dynamics. For the autonomous systems, one should note the analysis of the standard (Duffing and pendulum) equations including the solution to the ?weakened? 16 Hilbert's problem, and for the nonautonomous systems one should note the mathematical foundations of the theory of synchronization of oscillations (the existence of new regimes, and the passage of invariant tori across the resonance zones under the change of detuning). The presentation is accompanied by examples.

Author : Albert D Morozov
Publisher : World Scientific
Page : 340 pages
File Size : 49,6 Mb
Release : 1998-06-30
Category : Science
ISBN : 9789814498401

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Quasi-Conservative Systems: Cycles, Resonances and Chaos by Albert D Morozov Pdf

This monograph presents the theory of nonconservative systems close to nonlinear integrable ones. With the example of concrete quasi-conservative systems close to nonintegrable ones, the results of numerical analysis are given, and the problem of applying the small parameter method is analyzed. The fundamantal part of the book deals with the investigation of the perturbable systems. Both autonomous and nonautonomous (periodic in time) systems are considered. The global analysis of systems close to the two-dimensional Hamiltonian ones takes a central place in the text. This global analysis includes the solution to problems such as the limit cycles, resonances, and nonregular dynamics. For the autonomous systems, one should note the analysis of the standard (Duffing and pendulum) equations including the solution to the “weakened” 16 Hilbert's problem, and for the nonautonomous systems one should note the mathematical foundations of the theory of synchronization of oscillations (the existence of new regimes, and the passage of invariant tori across the resonance zones under the change of detuning). The presentation is accompanied by examples. Contents:Introduction and Review of Main ResultsConservative Nonlinear Systems:Integrable Nonlinear SystemsNon-Integrable Hamiltonian SystemsQuasi-Conservative Nonlinear Systems:Perturbed Autonomous Systems with One Degree of FreedomPeriodic Perturbations of Two-Dimensional Hamiltonian SystemsGeneralizations and ApplicationsNon-Quasi-Integrable Systems Readership: Nonlinear scientists, engineers and physicists. keywords:“The subject matter is well organized, each chapter building on the previous one.”Applied Mechanics Reviews “… the material is interesting and well presented, so this might be used as a textbook for a graduate course.”Mathematical Reviews

Author : Christos H. Skiadas,Charilaos Skiadas
Publisher : CRC Press
Page : 1003 pages
File Size : 47,7 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781315356549

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Handbook of Applications of Chaos Theory by Christos H. Skiadas,Charilaos Skiadas Pdf

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Author : Albert D Morozov,Timothy N Dragunov,Svetlana A Boykova,Olga V Malysheva
Publisher : World Scientific
Page : 272 pages
File Size : 43,7 Mb
Release : 1999-11-29
Category : Science
ISBN : 9789814494304

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Invariant Sets for Windows by Albert D Morozov,Timothy N Dragunov,Svetlana A Boykova,Olga V Malysheva Pdf

This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book. The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical systems to computer design. In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. The basic models of the diffusion equations are also considered. This part of the book is intended for a more advanced reader, with at least a BSc in Mathematics. Contents:Computer-Generated Invariant Sets:Description of WInSet ProgramList of the Built-in Equations, Maps and Fractals of WInSet. Main Invariant Sets of WInSetMathematical Description of Invariant Sets:Invariant Sets in Hamiltonian MechanicsArea-Preserving MapsNon-Conservative SystemsNon-Conservative MapsDiffusion Equations Readership: Mathematicians, physicists and engineers. Keywords:Dynamical Systems;Nonlinear Phenomena;Mappings;Invariant Sets;Resonances;Attractors;Fractals;Patterns;Computer Graphics

Author : Jan Awrejcewicz,Claude-henri Lamarque
Publisher : World Scientific
Page : 564 pages
File Size : 47,8 Mb
Release : 2003-07-14
Category : Mathematics
ISBN : 9789814485401

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Bifurcation And Chaos In Nonsmooth Mechanical Systems by Jan Awrejcewicz,Claude-henri Lamarque Pdf

This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Author : Zhanybai T. Zhusubaliyev,Erik Mosekilde
Publisher : World Scientific
Page : 377 pages
File Size : 41,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812384201

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Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by Zhanybai T. Zhusubaliyev,Erik Mosekilde Pdf

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Author : Marian Wiercigroch,Bram de Kraker
Publisher : World Scientific
Page : 466 pages
File Size : 49,8 Mb
Release : 2000
Category : Technology & Engineering
ISBN : 9810229275

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Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities by Marian Wiercigroch,Bram de Kraker Pdf

Annotation Consisting primarily of contributions written by engineers from Europe, Asia, and the US, this volume provides a general methodology for describing, solving, and analyzing discontinuous systems. The focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction, or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials, and dynamics of metal cutting. Of likely interest to new and experienced researchers working in the field of applied mathematics and physics, mechanical and civil engineering, and manufacturing. Lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 357 pages
File Size : 44,9 Mb
Release : 2017-04-10
Category : Mathematics
ISBN : 9783110335682

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Oscillations and Resonances by Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov Pdf

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators

Author : İlkay Bakırtaş
Publisher : BoD – Books on Demand
Page : 170 pages
File Size : 50,9 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9781789842555

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Perturbation Methods with Applications in Science and Engineering by İlkay Bakırtaş Pdf

The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

Author : Wanda Szempli
Publisher : World Scientific
Page : 117 pages
File Size : 46,7 Mb
Release : 2003
Category : Science
ISBN : 9789812386892

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Chaos Bifurcations and Fractals Around Us by Wanda Szempli Pdf

During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.

Author : Ralph Abraham,Yoshisuke Ueda
Publisher : World Scientific
Page : 231 pages
File Size : 45,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9789810244040

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The Chaos Avant-garde by Ralph Abraham,Yoshisuke Ueda Pdf

This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time ? two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler.

Author : Ralph Abraham,Yoshisuke Ueda
Publisher : World Scientific
Page : 231 pages
File Size : 40,8 Mb
Release : 2001-01-04
Category : Science
ISBN : 9789814492461

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Chaos Avant-garde, The: Memoirs Of The Early Days Of Chaos Theory by Ralph Abraham,Yoshisuke Ueda Pdf

This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time — two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler.

Author : Hendrik Nijmeijer,Alejandro Rodriguez-Angeles
Publisher : World Scientific
Page : 219 pages
File Size : 48,8 Mb
Release : 2003
Category : Technology & Engineering
ISBN : 9789812386052

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Synchronization of Mechanical Systems by Hendrik Nijmeijer,Alejandro Rodriguez-Angeles Pdf

The main goal of this book is to prove analytically and validate experimentally that synchronization in multi-composed mechanical systems can be achieved in the case of partial knowledge of the state vector of the systems, i.e. when only positions are measured. For this purpose, synchronization schemes based on interconnections between the systems, feedback controllers and observers are proposed. Because mechanical systems include a large variety of systems, and since it is impossible to address all of them, the book focuses on robot manipulators. Nonetheless the ideas developed here can be extended to other mechanical systems, such as mobile robots, motors and generators.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789814482301

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Bio-Inspired Emergent Control of Locomotion Systems by Anonim Pdf

Author : T. P. Leung,Hua-Shu Qin
Publisher : World Scientific
Page : 257 pages
File Size : 54,9 Mb
Release : 2001
Category : Technology & Engineering
ISBN : 9789810244422

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Advanced Topics in Nonlinear Control Systems by T. P. Leung,Hua-Shu Qin Pdf

Over the last 50 years or so, a number of textbooks, monographs and even popular books have been published on nonlinear control theory and design methods. In the area of classical control, for example, there exist books concerned with phase-plane analysis, describing function approach, absolute stability and so on. In the area of modern control there are those related to optimal control, using differential geometry and the differential algebra method, variable structural control, H-infinite control and so on. These books have been useful in promoting the development of automatic control science and technology. Since 1990 there have been many new results and contributions in the area of nonlinear control. This book introduces those topics to interested readers. It will also benefit automation engineers, researchers and scholars in related fields.