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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Equivariant Hopf bifurcation for neutral functional differential equations
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by Shangjiang Guo and Jeroen S. W. Lamb PDF
Proc. Amer. Math. Soc. 136 (2008), 2031-2041 Request permission

Abstract:

In this paper we employ an equivariant Lyapunov-Schmidt procedure to give a clearer understanding of the one-to-one correspondence of the periodic solutions of a system of neutral functional differential equations with the zeros of the reduced bifurcation map, and then set up equivariant Hopf bifurcation theory. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction.
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Additional Information
  • Shangjiang Guo
  • Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
  • MR Author ID: 679488
  • ORCID: 0000-0002-9114-5269
  • Email: shangjguo@hnu.cn
  • Jeroen S. W. Lamb
  • Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
  • MR Author ID: 319947
  • Email: jeroen.lamb@imperial.ac.uk
  • Received by editor(s): January 9, 2007
  • Published electronically: February 11, 2008
  • Additional Notes: The first author was supported in part by a China postdoctoral fellowship of the UK Royal Society, by the NNSF of China (Grant No. 10601016), by the program for New Century Excellent Talents in University of the Education Ministry of China (Grant No. [2007]70), and by the NSF of Hunan (Grant No. 06JJ3001).
    The second author was supported in part by the UK Engineering and Physical Sciences Research Council (EPSRC)
  • Communicated by: Carmen C. Chicone
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 2031-2041
  • MSC (2000): Primary 34K18; Secondary 34K20
  • DOI: https://doi.org/10.1090/S0002-9939-08-09280-0
  • MathSciNet review: 2383509