Bifurcations of periodic and antiperiodic orbits near an equilibrium in autonomous differential delay systems with one or two delays

We investigate bifurcations of periodic and antiperiodic solutions near equilibria for four classes of potential differential-delay equations involving one or two delays. By reformulating each system as a (generalized) Hamiltonian system, and applying the Hamiltonian bifurcation theory recently developed by the author we obtain bifurcation results of both Fadell–Rabinowitz and Rabinowitz type. The analysis relies on the computation of Maslov–type indices for fundamental solutions of the associated linear Hamiltonian systems.