[PDF] Strange Nonchaotic Attractors eBook

Author : Ulrike Feudel
Publisher : World Scientific
Page : 226 pages
File Size : 36,8 MB
Release : 2006
Category : Business & Economics
ISBN : 9812566333

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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. Key Features Topics are suitable for various disciplines dealing with nonlinear dynamics (mechanics, physics, nonlinear optics, hydrodynamics, chemical kinetics, etc.) A variety of theoretical tools is supplied to reveal different characteristics of strange nonchaotic behavior Readership: Graduate students and researchers in nonlinear science.

Author : Arkady S Pikovsky
Publisher : World Scientific
Page : 226 pages
File Size : 35,56 MB
Release : 2006-04-26
Category : Science
ISBN : 9814478768

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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 : Ulrike Feudel
Publisher : World Scientific
Page : 226 pages
File Size : 48,62 MB
Release : 2006
Category : Science
ISBN : 9812774408

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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.

Author : Tobias H. JŠger
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 47,98 MB
Release : 2009-08-07
Category : Mathematics
ISBN : 082184427X

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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'.

Author : Tomasz Kapitaniak
Publisher : World Scientific
Page : 101 pages
File Size : 19,63 MB
Release : 1994-01-28
Category : Science
ISBN : 9814502774

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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.

Author :
Publisher :
Page : 9 pages
File Size : 41,17 MB
Release : 1992
Category :
ISBN :

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Attractors which are not chaotic but nevertheless display strange geometric properties have been the subject of a number of studies since they were studied in certain quasiperiodically forced maps, by Grebogi et al. (Physica 13D, 26 (1984)). The attractors, as defined by these authors, are nonchaotic, since they are characterized by Lyapunov exponents which are smaller than zero; but are, however, strange since they display geometric properties unlike either limit cycles or quasiperiodic attractors. The attractors are produced by dissipative, nonlinear systems which are driven by two periodic external forces whose frequences are incommensurate. Strange nonchaotic attractors have been observed in numerical experiments with a variety of bistable and monostable nonlinear oscillators as well as in one ingenious experiment, designed by Ditto et al. (Phys. Rev. Lett. 65, 533 (1990)), using a forced, free standing beam whose mechanical properties could be externally controlled by magnetic fields. We study here a nonlinear oscillator with a multistable potential both numerically and with an analog simulator. The dynamics mimics that of the internal magnetic flux through an under damped, multistable, superconducting quantum interference device which is quasiperiodically forced. We report measurements and numerical computations of the power spectra, invariant density, and Poincare sections Precision numerical computations were used to study the Lyapunov exponents and to observe the destruction of a chaotic attractor and its replacement by a strange nonchaotic one.

Author : Julien C. Sprott
Publisher : M & T Books
Page : 426 pages
File Size : 35,23 MB
Release : 1993
Category : Computers
ISBN : 9781558512986

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Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.