Computation, continuation, and bifurcation of torus solutions for dissipative maps and ordinary differential equations
type: Item
instance of: scholarly article
title: Computation, continuation, and bifurcation of torus solutions for dissipative maps and ordinary differential equations
zbMATH Open document ID: 0617.34035
DOI: 10.1016/0167-2789(87)90105-9
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: The smooth and dissipative map \(s:X\to {\mathbb{R}}^ n\), \(X\subset {\mathbb{R}}^ n\) is called stroboscopic map, and \(\Sigma (x)=\{x,S(x),S^ 2(x),...\}\) strobed orbit. The author considers the stroboscopic maps derived from the underlying dynamical system governed by an iterative map or by ordinary differential equation (autonomous, periodically forced or bi-periodically forced). If a strobed orbit is periodic then S can be considered as a fixed point of the Poincaré map. This equivalence is generalized to be bi-periodic case and the fixed point is studied in dependence of any control parameter. Moreover, the author investigates the bifurcation of a torus solution from a periodic solution. He gives a method of localization of bifurcation points. The approach is algorithmic and illustrated by suitable numerical results.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C40
zbMATH DE Number: 4000431
zbMATH Keywords: stroboscopic map
zbMATH Keywords: strobed orbit
zbMATH Keywords: bifurcation
zbMATH Keywords: torus solution
zbMATH Keywords: numerical results
author: Christian Kaas-Petersen
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90105-9
OpenAlex ID: W2002576207
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description: scientific article; zbMATH DE number 4000431