The chaotic character of a two-species Bose-Einstein condensate in titled optical lattices is investigated. We obtained two perturbation solutions of the two coupled Gross-Pitaevskii equations by using the direct perturbation method. Theoretical analysis revels that the perturbation
solutions are chaotic ones because they satisfy the Melnikov chaos criterion, which indicates that the existence of chaotic behavior of the system. The corresponding numerical results agree well with the theoretical results. When the system parameters and initial conditions of the two coupled
condensates are identical, the phase portraits in the (u, du/dx) and (v, dv/dx) planes are identical and means that the two condensates are synchronized. However, they are different and asynchronous when there is any very small difference between these
parameters or initial conditions, which showed that the system parameters and initial conditions play a very important role in chaos control and synchronization.
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