Hopf bifurcation via the Poincaré procedure in delay-differential equations with two delays

In this work we apply the theory of h -asymptotic stability related to the Poincaré procedure to establish sufficient conditions for the existence of a Hopf bifurcation for a delayed differential equation with two constant delays, considering one of the delays as a parameter. An explicit calculation of the Poincaré constant G 4 is provided.