Chaotic Josephson effects in two-coupled Bose–Einstein condensates

We discuss the chaotic Josephson effects in two weakly coupled Bose–Einstein condensates (BECs). The boson Josephson junction (BJJ) dynamics in BECs is governed by the two-mode Gross–Pitaevskii equation. We obtained a perturbed chaotic solution of the BJJ equation by using the direct perturbation technique. Theoretical analysis reveals that the stable oscillating orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the Poincaré sections in the equivalent phase space (φ,φ˙) sensitively depends on the system parameter and initial conditions. Therefore, we can control the transitions between chaos and order by adjusting these parameters and conditions.