Direct computation of period doubling bifurcation points of large-scale systems of ODEs using a Newton-Picard method

Periodic solutions of certain large-scale systems of ODEs can be computed e fficiently using a hybrid Newton-Picard scheme, especially in a continuatio n context. In this paper we describe and analyse how this approach can be e xtended to the direct computation of period doubling bifurcation points. Th e Newton-Picard scheme is based on shooting and a splitting of the state sp ace in a low-dimensional subspace corresponding to the weakly stable and un stable modes and its orthogonal complement. The method avoids the computati on of the full monodromy matrix, which is present in the determining system for period doubling bifurcation points. Test results are presented that de monstrate the numerical properties.