Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, sad...

Full description

Saved in:
Bibliographic Details
Published in:Regular & chaotic dynamics 2011-02, Vol.16 (1-2), p.154-184
Main Authors: Vitolo, Renato, Broer, Henk, Simó, Carles
Format: Article
Language:English
Subjects:
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354711010060