Time delay in the swing equation: A variety of bifurcations.

The present paper addresses the swing equation with additional delayed damping as an example for pendulumlike systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. Insofar, the paper extends the results about the...