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

摘要

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.