Chaos Synchronization in Two Coupled Duffing Oscillators

We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x,u) and (y,v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.