Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuatio...

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Bibliographic Details

Main Authors:	Wulff, Claudia (Author), Hohmann, Andreas 1953- (Author), Deuflhard, Peter 1944-2019 (Author)
Format:	Book
Language:	English
Published:	Berlin Konrad-Zuse-Zentrum für Informationstechnik 1994
Series:	Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1994,12
Subjects:	Differential equations
Online Access:	Inhaltsverzeichnis
Summary:	Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with Z[subscript m]-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with n inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from O(n²) to O(n)."
Physical Description:	27 S. graph. Darst.