Hopf bifurcation calculations for functional differential equations
The author presents an alternate method for analyzing the Hopf bifurcation problem in a class of functional differential equations with unbounded delay: \(\dot y(t)=\int^{0}_{\infty}d\eta (\alpha;s)y_ t(s)+H(\alpha;y_ t).\) An advantage of this method over previous ones for example by \textit{S.-N. Chow} and \textit{J. Mallet-Paret} [J. Differ. Equations 26, 112-159 (1977; Zbl 0367.34033)] is that it avoids all reference to the infinite-dimensional nature of the problem. Its importance lies both in its generality and its relative ease of applications. The method is based on Lyapunov-Schmidt means and is motivated by the work of \textit{J. C. De Oliveira} and \textit{J. K. Hale} [Tôhoku Math. J., II. Ser. 32, 577-592 (1980; Zbl 0454.34035)].
scientific article; zbMATH DE number 3951051
scientific article