Js. Fang et al., An analytical study for controlling chaos in duffing oscillator with weak periodic perturbation, CHIN PHYS L, 18(3), 2001, pp. 334-336
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 perio
dic orbits are embedded in the Melnikov chaotic attractor. The correspondin
g numerical results show that fitting control parameters into the stability
conditions can control chaos in the system, and the phase difference betwe
en the two sinusoidal forces added to the Duffing equation plays an importa
nt role in controlling chaos.