Time Delay in the Swing Equation: A Variety of Bifurcations
Abstract
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like 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. In so far the paper extends results about stability switching of equilibria in linear time delay systems from Cooke and Grossman. In addition to the analytical results, periodic solutions are numerically dealt with. The numerical results demonstrate how a variety of qualitative behaviors is generated in the simple swing equation by only introducing time delay in a damping term.
Keywords
Cite
@article{arxiv.1908.07996,
title = {Time Delay in the Swing Equation: A Variety of Bifurcations},
author = {Tessina H. Scholl and Lutz Gröll and Veit Hagenmeyer},
journal= {arXiv preprint arXiv:1908.07996},
year = {2019}
}
Comments
12 pages, 6 figures, "The following article has been accepted by 'Chaos: An Interdisciplinary Journal of Nonlinear Science'. After it is published, it will be found at https://aip.scitation.org/journal/cha."