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

Abstract

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.

Latex, 96 pages. Sufficient conditions under weaker assumptions have been added to the relevant theorems and corollaries, with corresponding adjustments made to their statements and proofs. Typos and a mistake in the proof of Theorem 6.3 have been corrected