Open AccessBook
Nonlinear Dynamics and Chaos
Reads0
Chats0
TLDR
In this paper, the authors present a broad overview of nonlinear phenomena point attractors in autonomous systems, including limit cycles in autonomous system, and chaotic behaviour of one-and two-dimensional maps.Abstract:
Preface. Preface to the First Edition. Acknowledgements from the First Edition. Introduction PART I: BASIC CONCEPTS OF NONLINEAR DYNAMICS An overview of nonlinear phenomena Point attractors in autonomous systems Limit cycles in autonomous systems Periodic attractors in driven oscillators Chaotic attractors in forced oscillators Stability and bifurcations of equilibria and cycles PART II ITERATED MAPS AS DYNAMICAL SYSTEMS Stability and bifurcation of maps Chaotic behaviour of one--and two--dimensional maps PART III FLOWS, OUTSTRUCTURES AND CHAOS The Geometry of Recurrence The Lorenz system Rosslers band Geometry of bifurcations PART IV APPLICATIONS IN THE PHYSICAL SCIENCES Subharmonic resonances of an offshore structure Chaotic motions of an impacting system Escape from a potential well Appendix. Illustrated Glossary. Bibliography. Online Resource. Index.read more
Citations
More filters
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Journal ArticleDOI
Articulatory gestures as phonological units
TL;DR: It is argued that dynamically defined articulatory gestures are the appropriate units to serve as the atoms of phonological representation, and the phonological notation developed for the gestural approach might usefully be incorporated, in whole or in part, into other phonologies.
Journal ArticleDOI
Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people.
TL;DR: In this article, the authors investigated the differential stability of the 2 phase modes and found that the asymmetric phase mode was less stable as the frequency of oscillation increased, while the symmetric mode was more comfortable than the alternate phase mode.
Journal ArticleDOI
Directing attention to movement effects enhances learning: a review.
Gabriele Wulf,Wolfgang Prinz +1 more
TL;DR: Preliminary evidence is presented indicating that an internal attentional focus constrains the motor system by interfering with natural control processes, whereas an external focus seems to allow automatic control processes to regulate the movements.
Journal ArticleDOI
Control of multistability
TL;DR: In this paper, the authors review the most representative control strategies and discuss their theoretical background and experimental realization, and discuss the importance of multistability control in applied nonlinear science.