Strange nonchaotic attractors : dynamics between order and chaos in quasiperiodically forced systems / Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky.

Format:

Book

Author/Creator:

Feudel, Ulrike.

Contributor:

Kuznet︠s︡ov, S. P. (Sergeĭ Petrovich), 1951-

Pikovsky, Arkady, 1956-

Series:

World Scientific series on nonlinear science. Monographs and treatises ; Series A, v. 56.

World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 56

Language:

English

Subjects (All):

Attractors (Mathematics).

Chaotic behavior in systems.

Differentiable dynamical systems.

Nonlinear systems.

Physical Description:

1 online resource (226 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2006.

Language Note:

English

Summary:

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

Contents:

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

5.2.2 Spectral properties of fractal tori

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611919450

9781281919458

1281919454

9789812774408

9812774408

OCLC:

879023955