An analysis of truncated fractal growths in the stability boundaries of three-node swing equations

A second-order nonautonomous ordinary differential equation (the transiently forced pendulum system), is studied and the existence of fractally intertwined stability domains is reported for certain ranges of parameters in the time-dependent forcing function. The analysis is extended to a modified version of Sitnikov's three-body problem in celestial mechanics. Parallels are drawn with the three-body problem and the swing dynamics of a three-generator electric power system.>