Global Hopf bifurcation for differential equations with state-dependent delay

Abstract We develop a global Hopf bifurcation theory for a system of functional differential equations with state-dependent delay. The theory is based on an application of the homotopy invariance of S 1 -equivariant degree using the formal linearization of the system at a stationary state. Our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local Hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state-dependent delay.

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