Preface |
Preface to the First Edition |
Acknowledgements from the First Edition |
Introduction / 1: |
Historical background / 1.1: |
Chaotic dynamics in Duffing's oscillator / 1.2: |
Attractors and bifurcations / 1.3: |
Basic Concepts of Nonlinear Dynamics / Part I: |
An overview of nonlinear phenomena / 2: |
Undamped, unforced linear oscillator / 2.1: |
Undamped, unforced nonlinear oscillator / 2.2: |
Damped, unforced linear oscillator / 2.3: |
Damped, unforced nonlinear oscillator / 2.4: |
Forced linear oscillator / 2.5: |
Forced nonlinear oscillator: periodic attractors / 2.6: |
Forced nonlinear oscillator: chaotic attractor / 2.7: |
Point attractors in autonomous systems / 3: |
The linear oscillator / 3.1: |
Nonlinear pendulum oscillations / 3.2: |
Evolving ecological systems / 3.3: |
Competing point attractors / 3.4: |
Attractors of a spinning satellite / 3.5: |
Limit cycles in autonomous systems / 4: |
The single attractor / 4.1: |
Limit cycle in a neural system / 4.2: |
Bifurcations of a chemical oscillator / 4.3: |
Multiple limit cycles in aeroelastic galloping / 4.4: |
Topology of two-dimensional phase space / 4.5: |
Periodic attractors in driven oscillators / 5: |
The Poincare map / 5.1: |
Linear resonance / 5.2: |
Nonlinear resonance / 5.3: |
The smoothed variational equation / 5.4: |
Variational equation for subharmonics / 5.5: |
Basins of attraction by mapping techniques / 5.6: |
Resonance of a self-exciting system / 5.7: |
The ABC of nonlinear dynamics / 5.8: |
Chaotic attractors in forced oscillators / 6: |
Relaxation oscillations and heartbeat / 6.1: |
The Birkhoff-Shaw chaotic attractor / 6.2: |
Systems with nonlinear restoring force / 6.3: |
Stability and bifurcations of equilibria and cycles / 7: |
Liapunov stability and structural stability / 7.1: |
Centre manifold theorem / 7.2: |
Local bifurcations of equilibrium paths / 7.3: |
Local bifurcations of cycles / 7.4: |
Basin changes at local bifurcations / 7.5: |
Prediction of incipient instability / 7.6: |
Iterated Maps as Dynamical Systems / Part II: |
Stability and bifurcation of maps / 8: |
Stability of one-dimensional maps / 8.1: |
Bifurcations of one-dimensional maps / 8.3: |
Stability of two-dimensional maps / 8.4: |
Bifurcations of two-dimensional maps / 8.5: |
Basin changes at local bifurcations of limit cycles / 8.6: |
Chaotic behaviour of one- and two-dimensional maps / 9: |
General outline / 9.1: |
Theory for one-dimensional maps / 9.2: |
Bifurcations to chaos / 9.3: |
Bifurcation diagram of one-dimensional maps / 9.4: |
Henon map / 9.5: |
Flows, Outstructures, and Chaos / Part III: |
The geometry of recurrence / 10: |
Finite-dimensional dynamical systems / 10.1: |
Types of recurrent behaviour / 10.2: |
Hyperbolic stability types for equilibria / 10.3: |
Hyperbolic stability types for limit cycles / 10.4: |
Implications of hyperbolic structure / 10.5: |
The Lorenz system / 11: |
A model of thermal convection / 11.1: |
First convective instability / 11.2: |
The chaotic attractor of Lorenz / 11.3: |
Geometry of a transition to chaos / 11.4: |
Rossler's band / 12: |
The simply folded band in an autonomous system / 12.1: |
Return map and bifurcations / 12.2: |
Smale's horseshoe map / 12.3: |
Transverse homoclinic trajectories / 12.4: |
Spatial chaos and localized buckling / 12.5: |
Geometry of bifurcations / 13: |
Local bifurcations / 13.1: |
Global bifurcations in the phase plane / 13.2: |
Bifurcations of chaotic attractors / 13.3: |
Applications in the Physical Sciences / Part IV: |
Subharmonic resonances of an offshore structure / 14: |
Basic equation and non-dimensional form / 14.1: |
Analytical solution for each domain / 14.2: |
Digital computer program / 14.3: |
Resonance response curves / 14.4: |
Effect of damping / 14.5: |
Computed phase projections / 14.6: |
Multiple solutions and domains of attraction / 14.7: |
Chaotic motions of an impacting system / 15: |
Resonance response curve / 15.1: |
Application to moored vessels / 15.2: |
Period-doubling and chaotic solutions / 15.3: |
Escape from a potential well / 16: |
Analytical formulation / 16.1: |
Overview of the steady-state response / 16.3: |
The two-band chaotic attractor / 16.4: |
Resonance of the steady states / 16.5: |
Transients and basins of attraction / 16.6: |
Homoclinic phenomena / 16.7: |
Heteroclinic phenomena / 16.8: |
Indeterminate bifurcations / 16.9: |
Appendix |
Illustrated Glossary |
Bibliography |
Online Resources |
Index |
Preface |
Preface to the First Edition |
Acknowledgements from the First Edition |
Introduction / 1: |
Historical background / 1.1: |
Chaotic dynamics in Duffing's oscillator / 1.2: |