Strange Nonchaotic Attractors : Dynamics Between Order and Chaos in Quasiperiodically Forced Systems.

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 S...

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Bibliographic Details
Main Author: Feudel, Ulrike
Other Authors: Kuznetsov, Sergey, Pikovsky, Arkady
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2006.
Series:World Scientific series on nonlinear science. Monographs and treatises.
Subjects:
Online Access:Click for online access
Table of Contents:
  • Preface ; 1 Introduction ; 1.1 Periodicity and quasiperiodicity ; 1.2 Robustness of quasiperiodic motions ; 1.3 Strange nonchaotic attractors ; 1.4 What is in the book ; 2 Models ; 2.1 Differential equations and maps ; 2.2 Quasiperiodically forced one-dimensional maps.
  • 2.2.1 GOPY model (modulated pitchfork map) 2.2.2 Forced circle map ; 2.2.3 Skew shift ; 2.2.4 Forced logistic map ; 2.2.5 Harper model ; 2.3 Quasiperiodically forced high-dimensional maps ; 2.4 Quasiperiodically forced continuous-time systems ; 2.4.1 Forced overdamped pendulum.
  • 2.4.2 Forced Duffing oscillator 2.5 Experiments ; 2.6 Bibliographic notes ; 3 Rational approximations ; 3.1 Properties of rational approximations of irrationals ; 3.2 Rational approximations to quasiperiodic forcing ; 3.3 Checking strangeness of SNA through rational approximations.
  • 3.3.1 Rational approximations to a smooth attractor 3.3.2 Rational approximations to an SNA: An example ; 3.3.3 Rational approximations to an SNA: General consideration ; 3.3.4 Different examples ; 3.4 Bibliographic notes ; 4 Stability and Instability ; 4.1 Theoretical consideration.
  • 4.2 Numerical examples 4.2.1 Discrete time mappings ; 4.2.2 Continuous time systems ; 4.3 Bibliographic notes ; 5 Fractal and statistical properties ; 5.1 Fractal properties of SNA ; 5.2 Correlations and spectra of SNA ; 5.2.1 Power spectra of regular and irregular motions.