Asymmetric Duffing oscillator: the birth and build-up of period doubling

In this work, we investigate the period doubling phenomenon in the periodically forced asymmetric Duffing oscillator. We use the known steady-state asymptotic solution – the amplitude-frequency implicit function – and known criterion for the existence of period doubling. Working in the framework of differential properties of implicit functions we derive analytical formulas for the birth of period-doubled solutions.