DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
type: Item
instance of: scholarly article
title: DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
zbMATH Open document ID: 0575.65076
DOI: 10.1016/0021-9991(84)90005-6
author: Martin Holodniok
author: M. Kubíček
published in: Journal of Computational Physics
publication date: 1984-01-01T00:00:00Z
review text: An algorithm for the continuation of periodic solutions of ODE was derived and tested. The algorithm is based on the shooting method and a standard continuation algorithm. Variational variables are used to compute the Jacobi matrix. The starting point on the periodic orbit is adaptively changed in the algorithm by fixing one component of the solution. Stability of periodic solutions along the continuous branch of solutions is determined by computing characteristic multipliers. Without difficulty the algorithm crosses limit points and at bifurcation points, double-period bifurcation points, and points of tori bifurcation it proceeds along the original branch of solutions. The usefulness of the algorithm is demonstrated in two examples. One of them describes two stirred tank reactors with mutual mass exchange, the other one is the Lorenz model of turbulence.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34-04
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 3919697
zbMATH Keywords: continuation of periodic solutions
zbMATH Keywords: shooting method
zbMATH Keywords: continuous branch of solutions
zbMATH Keywords: characteristic multipliers
zbMATH Keywords: bifurcation points
MaRDI profile type: Publication
full work available at URL: 0021-9991(84)90005-6
OpenAlex ID: W1995459307
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description: scientific article; zbMATH DE number 3919697