On the influence of a constant force on the appearance of period-doubling bifurcations and chaos in a harmonically excited pure cubic oscillator

A pure cubic oscillator with a constant and a harmonic force acting on it, which represents a nonlinear asymmetric system, is considered. Building on previous studies on the matter, analytical and numerical approaches are used to examine and illustrate its dynamics related to the phenomenon of period-doubling bifurcations and their development into chaos for different values of the constant force. The region of control parameters in which this scenario is possible is determined and discussed with a view to revisiting literature results and to giving novel and deeper insights into the phenomenon related to the influence of the magnitude of the constant force and certain resonances.