Website Search
Find information on spaces, staff, and services.
Catalog Search
Books
Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems
- Author / Creator
- Available as
- Online
- 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 dissipa...
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
Details
- Creator
- Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- New Jersey : World Scientific, c2006
- Physical Details
-
- 1 online resource (226 p.)
- ISBNs
- 1281919454, 9786611919450, 9812774408, 9812566333
- OCLC
- ocn879023955
- Description based upon print version of record.
- Includes bibliographical references and index.
- English
- 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