Equivariant Hopf bifurcation for functional differential equations of mixed type
The paper proves the equivariant Hopf bifurcation theorem for functional-differential equations of mixed type (that is, equations, for example, of the form \(\dot x(t)=f(x(t),x(t-\tau_1),x(t+\tau_2))\) with \(\tau_1\), \(\tau_2>0\)) with symmetry. By resorting to Lyapunov-Schmidt reduction techniques on spaces of periodic functions, the paper avoids all difficulties associated with mixed-type equations (on the space of periodic functions future and past are indistinguishable). In fact, the results and arguments in the paper are identical to the case containing only delays, for example, considered by \textit{S. Gou} and \textit{L. Huang} [Physica D 183, No. 1--2, 19--44 (2003; Zbl 1041.68079)].
functional differential equations of mixed type
scientific article; zbMATH DE number 5864286