Strange Nonchaotic Attractors
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Strange Nonchaotic Attractors
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language : en
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Strange Nonchaotic Attractors
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Author : Ulrike Feudel
language : en
Publisher: World Scientific
Release Date : 2006
Strange Nonchaotic Attractors written by Ulrike Feudel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
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. Sample Chapter(s). Chapter 1: Introduction (122 KB). Contents: Models; Rational Approximations; Stability and Instability; Fractal and Statistical Properties; Bifurcations in Quasiperiodically Forced Systems and Transitions to SNA; Renormalization Group Approach to the Onset of SNA in Maps with the Golden-Mean Quasiperiodic Driving. Readership: Graduate students and researchers in nonlinear science.
Attractors Of Quasiperiodically Forced Systems
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Author : Tomasz Kapitaniak
language : en
Publisher: World Scientific
Release Date : 1994-01-28
Attractors Of Quasiperiodically Forced Systems written by Tomasz Kapitaniak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-28 with Science categories.
This book discusses the influence of quasiperiodic force on dynamical system. With this type of forcing, different types of attractors are possible, for example, strange nonchaotic attractors which have some unusual properties. The main part of this book is based on the authors' recent works, but it also presents the results which are the combined achievements of many investigators. Contents:IntroductionAttractors of Dynamical SystemsStrange Nonchaotic AttractorsInhibition of Chaotic Behaviour in Coupled Geophysical ModelsExperimental System with Dry Friction Readership: Scientists interested in chaos and nonlinear science. keywords: “… useful as a first reading in this particular subfield of nonlinear dynamics.” Mathematical Reviews
The Creation Of Strange Non Chaotic Attractors In Non Smooth Saddle Node Bifurcations
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Author : Tobias H. Jger
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-07
The Creation Of Strange Non Chaotic Attractors In Non Smooth Saddle Node Bifurcations written by Tobias H. Jger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-07 with Mathematics categories.
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Chaos And Nonlinear Mechanics Proceedings Of Euromech Colloquium 308 Chaos And Noise In Dynamical Systems
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Author : Kapitaniak Tomasz
language : en
Publisher: World Scientific
Release Date : 1994-10-28
Chaos And Nonlinear Mechanics Proceedings Of Euromech Colloquium 308 Chaos And Noise In Dynamical Systems written by Kapitaniak Tomasz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-28 with categories.
This volume contains a selection of papers presented at Euromech Colloquium 308 — Chaos and Noise in Dynamical Systems.Roughly speaking, a chaotic solution to an ordinary differential equation is aperiodic and “looks like” a stochastic process. On the other hand, the theory of probability and stochastic processes was developed to describe complicated irregular phenomena taking place in the real world, which in most cases are chaotic. This observation led to the idea of bringing together experts on both nonlinear chaotic and stochastic systems for the conference. Equal attention was given to recent theoretical results and practical applications.The revised and updated papers in this volume are grouped in the following sections: Theory of Chaotic Systems; Stochastic Systems; Spatiotemporal Systems and Fluid Dynamics; Numerical Tools; and Practical Applications. Each section starts with a short introduction and a brief summary of the presented papers.
Chaotic Oscillators
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Author : T Kapitaniak
language : en
Publisher: World Scientific
Release Date : 1992-11-30
Chaotic Oscillators written by T Kapitaniak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-30 with Medical categories.
This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection. Contents: Chaos before Chaos:Frequency Demultiplication (B Van der Pol & J Van der Mark)Description and Quantification of Chaotic Behavior:Geometry from a Time Series (N H Packard et al.)Analytical Methods:A Partial Differential Equation with Infinitely Many Periodic Orbits: Chaotic Oscillations of a Forced Beam (P Holmes & J Marsden)Classical Nonlinear Oscillators: Duffing, Van der Pol and Pendulum:Universal Scaling Property in Bifurcation Structure of Duffing's and Generalized Duffing's Equations (S Sato et al.)Other Oscillatory Systems:Complex Dynamics of Compliant Off-Shore Structures (J M T Thompson)Chaos in Noisy Systems:Fluctuations and the Onset of Chaos (J P Crutchfield & B A Huberman)Strange Nonchaotic Attractors:Dimensions of Strange Nonchaotic Attractors (M Ding et al.)Spatial Chaos:Chaos as a Limit in a Boundary Value Problem (C Kahlert & O E Rössler)Fractal Basin Boundaries:Fractal Basin Boundaries and Homoclinic Orbit for Periodic Motion in a Two-Well Potential (F C Moon & G-H Li)and other papers Readership: Nonlinear scientists, applied mathematicians, engineers and physicists. keywords:
Chaotic Oscillations In Mechanical Systems
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Author : Tomasz Kapitaniak
language : en
Publisher: Manchester University Press
Release Date : 1991
Chaotic Oscillations In Mechanical Systems written by Tomasz Kapitaniak and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Health & Fitness categories.
Chaotic Oscillators
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Author : Tomasz Kapitaniak
language : en
Publisher: World Scientific
Release Date : 1992
Chaotic Oscillators written by Tomasz Kapitaniak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Chaotic Evolution And Strange Attractors
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Author : David Ruelle
language : en
Publisher: Cambridge University Press
Release Date : 1989-09-07
Chaotic Evolution And Strange Attractors written by David Ruelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-07 with Mathematics categories.
This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Mathematical Methods In Contemporary Chemistry
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Author : Kuchanov
language : en
Publisher: CRC Press
Release Date : 1996-03-20
Mathematical Methods In Contemporary Chemistry written by Kuchanov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-20 with Mathematics categories.