Chaos crisis in coupled Duffing's systems with initial phase difference

The dynamics of coupled Duffing's oscillators with initial phase difference is investigated in this Letter. For the averaged equations, different equilibrium points can be observed, the number of which may vary with the parameters. The stable equilibrium points, corresponding to the periodic motion of the original coupled oscillators, may coexist with different patterns of dynamics, including chaos. Furthermore, two different chaotic attractors associated with different attracting basin coexist for certain parameter conditions, which may interact with each other to form an enlarged chaotic attractor. Several new dynamical phenomena such as boundary chaos crises have been predicted as the initial phase difference varies.