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Computation of periodic solution bifurcations in ODEs using bordered systems

Doedel, E. J. and Govaerts, W. and Kuznetsov, Yu. A. (2003) Computation of periodic solution bifurcations in ODEs using bordered systems. SIAM Journal on Numerical Analysis, 41 (2). pp. 401-435. ISSN 0036-1429. doi:10.1137/S0036142902400779.

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We consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous ODEs, namely the fold, the period-doubling (or flip) bifurcation, and the torus (or Neimark–Sacker) bifurcation. In the fold and flip cases we append one scalar equation to the standard periodic BVP that defines the periodic solution; in the torus case four scalar equations are appended. Evaluation of these scalar equations and their derivatives requires the solution of linear BVPs, whose sparsity structure (after discretization) is identical to that of the linearization of the periodic BVP. Therefore the calculations can be done using existing numerical linear algebra techniques, such as those implemented in the software AUTO and COLSYS.

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Additional Information:© 2003 Society for Industrial and Applied Mathematics. Received by the editors January 9, 2002; accepted for publication (in revised form) October 16, 2002; published electronically April 23, 2003.
Subject Keywords:bifurcations, periodic solutions, continuation, boundary value problems
Issue or Number:2
Record Number:CaltechAUTHORS:DOEsiamjna03
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:565
Deposited By: Tony Diaz
Deposited On:08 Aug 2005
Last Modified:08 Nov 2021 19:03

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