An Analytical Study for Controlling Chaos in Duffing Oscillator with Weak Periodic Perturbation

We obtain a general unstable periodic solution near the homoclinic orbit of the Duffing oscillator with weak periodic perturbation by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractor. The corresponding numerical results show that fitting control parameters into the stability conditions can control chaos in the system, and the phase difference between the two sinusoidal forces added to the Duffing equation plays an important role in controlling chaos.