Paper

Nonintegrability of the unfolding of the fold-Hopf bifurcation

Published 2 January 2018 • © 2018 IOP Publishing Ltd & London Mathematical Society
, , Citation Kazuyuki Yagasaki 2018 Nonlinearity 31 341 DOI 10.1088/1361-6544/aa92e8

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yagasaki@amp.i.kyoto-u.ac.jp

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1 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan

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Dates

  1. Received 2 June 2017
  2. Accepted 12 October 2017
  3. Published

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0951-7715/31/2/341

Abstract

We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales–Ramis–Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.

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10.1088/1361-6544/aa92e8