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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivariant Hopf bifurcation for neutral functional differential equations


Authors: Shangjiang Guo and Jeroen S. W. Lamb
Journal: Proc. Amer. Math. Soc. 136 (2008), 2031-2041
MSC (2000): Primary 34K18; Secondary 34K20
Published electronically: February 11, 2008
MathSciNet review: 2383509
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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
Email: shangjguo@hnu.cn

Jeroen S. W. Lamb
Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Email: jeroen.lamb@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09280-0
PII: S 0002-9939(08)09280-0
Keywords: Lyapunov-Schmidt reduction, equivariant Hopf bifurcation, neutral functional differential equations, Lie group
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.