Attractors of Quasiperiodically Forced Systems

The following sections are included:

• Contents

• Preface

Recently a growing interest has been observed in the study of forced dynamical systems with multiple incommensurate forcing terms. Forcing at (at least) two irrationally related frequencies is common in engineering systems; indeed forcing at a single frequency is likely to be the exception rather than the rule. A criterion, in naturally occurring dynamical systems, physical or biological, is that a multi-peaked spectrum of forcing is to be expected. Quasiperiodically forced systems are investigated from mathematical, physical and more recently from mechanical engineering standpoints.

The following sections are included:

• Basic Attractors

• Poincaré Map

• Lyapunov Exponents and their Calculation

The following sections are included:

• Examples
  • Quasiperiodically Forced Van der Pol Oscillator
  • Quasiperiodically Forced Chemical System
  • Quasiperiodic circle map

• Prediction of Non-Chaotic Strange Attractors
  • Existence of Quasiperiodic Solutions
  • Hopf Bifurcation in the Averaged System

• Distinction Between Strange Chaotic and Strange Nonchaotic Attractors

• Strange nonchaotic transients

• Models of Strange Nonchaotic Attractors
  • Geometrical Model
  • Dynamical model

The following sections are included:

• Chaos and Aperiodicity in Geophysical Models

• The Salzman Oscillator

• El Nino - Southern Oscillation

The following sections are included:

• Experiments

• Properties of the Power Spectra

• Behaviour of the Friction Force

• Model for the Observed Behaviour

The following sections are included:

• References

• Index