Duffing equation with two periodic forcings: The phase effect

A weak additional sinusoidal perturbation is applied to the periodically forced nonlinear oscillator to suppress chaos. Numerical simulations show that the phase difference between the two sinusoidal forces plays a very important role in controlling chaos. When the frequencies of these forces deviate from the resonance condition slightly, a different type of intermittency, alternation from regular motion to chaotic motion (called breather here), is observed. If the phase difference follows a Wiener process, conventional intermittency is observed.