Quasi Conservative Systems Cycles Resonances And Chaos
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Quasi Conservative Systems Cycles Resonances And Chaos
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Author : Albert D Morozov
language : en
Publisher: World Scientific
Release Date : 1998-06-30
Quasi Conservative Systems Cycles Resonances And Chaos written by Albert D Morozov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-30 with Science categories.
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.
Invariant Sets For Windows Resonance Structures Attractors Fractals And Patterns
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Author : Svetlana A Boykova
language : en
Publisher: World Scientific
Release Date : 1999-11-29
Invariant Sets For Windows Resonance Structures Attractors Fractals And Patterns written by Svetlana A Boykova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-29 with Science categories.
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.
Bifurcation And Chaos In Nonsmooth Mechanical Systems
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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 2003-07-14
Bifurcation And Chaos In Nonsmooth Mechanical Systems written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-14 with Mathematics categories.
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.
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities
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Author : Bram De Kraker
language : en
Publisher: World Scientific
Release Date : 2000-04-28
Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities written by Bram De Kraker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-28 with Technology & Engineering categories.
Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main 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.
Quasi Conservative Systems
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Author : Albert D. Morozov
language : en
Publisher: World Scientific
Release Date : 1998
Quasi Conservative Systems written by Albert D. Morozov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
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.
Oscillations And Resonances
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Author : Sergey G. Glebov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Oscillations And Resonances written by Sergey G. Glebov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
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
Handbook Of Applications Of Chaos Theory
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Author : Christos H. Skiadas
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Handbook Of Applications Of Chaos Theory written by Christos H. Skiadas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
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.
Chaos Bifurcations And Fractals Around Us
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Author : Wanda Szempli
language : en
Publisher: World Scientific
Release Date : 2003
Chaos Bifurcations And Fractals Around Us written by Wanda Szempli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
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.
Perturbation Methods With Applications In Science And Engineering
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Author : İlkay Bakırtaş
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-10-17
Perturbation Methods With Applications In Science And Engineering written by İlkay Bakırtaş and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Mathematics categories.
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.