Control of Homoclinic Chaos by Weak Periodic Perturbations PDF Download
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Author: Ricardo Chac¢n
Publisher: World Scientific
ISBN: 9812380426
Category : Science
Languages : en
Pages : 240
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Book Description
This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression?enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression?enhancement of the initial chaos.The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel?Kontorova chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets.
Author: Ricardo Chac¢n
Publisher: World Scientific
ISBN: 9812380426
Category : Science
Languages : en
Pages : 240
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Book Description
This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression?enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression?enhancement of the initial chaos.The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel?Kontorova chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets.
Author: Ricardo Chac¢n
Publisher: World Scientific
ISBN: 9812703519
Category : Science
Languages : en
Pages : 238
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Book Description
This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppressionOCoenhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppressionOCoenhancement of the initial chaos. The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in FrenkelOCoKontorova chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets."
Author: Michal Fečkan
Publisher: Springer Science & Business Media
ISBN: 3642182690
Category : Science
Languages : en
Pages : 387
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Book Description
"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.
Author: Miguel Angel Fern ndez Sanju n
Publisher: World Scientific
ISBN: 9814291692
Category : Science
Languages : en
Pages : 440
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Book Description
This book provides a collection of research papers on one of the topics where the applications of chaos have been more fruitful: controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics. Recent Progress in Controlling Chaos will provide an overview of the recent progress in this field, which will be very useful for students and researchers. The authors of these research works are prominent in their areas of specialization, and they offer an excellent state-of-the-art of this field and its most recent developments and progress.
Author: Wing-Kuen Ling
Publisher: World Scientific
ISBN: 9812790578
Category : Technology & Engineering
Languages : en
Pages : 281
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Book Description
In this book, leading researchers present their current work in the challenging area of chaos control in nonlinear circuits and systems, with emphasis on practical methodologies, system design techniques and applications. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this area. The scope and aim of this book are to bridge the gap between chaos control methods and circuits and systems. It is an ideal starting point for anyone who needs a fundamental understanding of controlling chaos in nonlinear circuits and systems.
Author: Marco Thiel
Publisher: Springer
ISBN: 3642046290
Category : Science
Languages : en
Pages : 300
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Book Description
This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Author: A. Fradkov
Publisher: Springer
ISBN: 3540462775
Category : Science
Languages : en
Pages : 248
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Book Description
Cybernetical physics borrows methods from both theoretical physics and control engineering. It deals with the control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behavior or similar features that defy traditional control techniques. This book fully details this new discipline.
Author: Ivana Kovacic
Publisher: John Wiley & Sons
ISBN: 0470977833
Category : Science
Languages : en
Pages : 335
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Book Description
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
Author: Arkady S Pikovsky
Publisher: World Scientific
ISBN: 9814478768
Category : Science
Languages : en
Pages : 226
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Book Description
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed.
Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9814474649
Category : Science
Languages : en
Pages : 318
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Book Description
This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics.This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background.
