Symmetric Hopf bifurcation in implicit neutral functional differential equations: Equivariant degree approach

In this paper, we develop a general framework for studying symmetric Hopf bifurcation phenomenon for (symmetric) implicit neutral functional differential equations (in short, INFDEs) satisfying appropriate compactness and nonexpansiveness conditions. The main abstract result, obtained by means of th...

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Bibliographic Details
Published in:Journal of fixed point theory and applications 2014-12, Vol.16 (1-2), p.109-147
Main Authors: Balanov, Zalman, Krawcewicz, Wieslaw, Li, Zhichao
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we develop a general framework for studying symmetric Hopf bifurcation phenomenon for (symmetric) implicit neutral functional differential equations (in short, INFDEs) satisfying appropriate compactness and nonexpansiveness conditions. The main abstract result, obtained by means of the twisted equivariant degree theory, establishes sufficient conditions for the occurrence of the Hopf bifurcation and provides a complete description of symmetric properties of bifurcating branches. The abstract result is supported by a concrete example of an INFDE admitting countably many Hopf bifurcation points and respecting D 24 -symmetries.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-015-0209-4