Improved homoclinic predictor for Bogdanov-Takens bifurcation

Iouri Aleksandrovitsj Kouznetsov, H.G.E. Meijer, B. Al Hdaibat, W. Govaerts

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Abstract

An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical "blow-up" technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit rst- and second-order corrections of the unperturbed homoclinic orbit and parameter value. To obtain the normal form on the center manifold, we apply the standard parameter-dependent center manifold reduction combined with the normalization, that is based on the Fredholm solvability of the homological equation. By systematically solving all linear systems appearing from the homological equation, we remove an ambiguity in the parameter transformation existing in the literature. The actual implementation of the improved predictor in MatCont and numerical examples illustrating its eciency are discussed.
Original languageUndefined
Pages (from-to)1450057
Number of pages12
JournalInternational journal of bifurcation and chaos in applied sciences and engineering
Volume24
Issue number4
DOIs
Publication statusPublished - 24 Apr 2014

Keywords

  • EWI-24077
  • Homoclinic orbit
  • Normal form
  • MatCont
  • IR-90569
  • Center manifold
  • Bogdanov-Takens bifurcation
  • METIS-303975

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