Stability and chaotic behavior of a two-component Bose–Einstein condensate

We investigate the stability and chaotic behavior of a periodically driven Bose–Einstein condensate (BEC) with two hyperfine states. The effects of the population transfer K and relative energy fluctuation γ between the two hyperfine states are demonstrated analytically and numerically. The stability analysis shows that the steady-state relative population will appear the tuning-fork bifurcation, when the physical parameters are changed to some critical values. Meanwhile, the dependence of the macroscopic quantum self-trapping (MQST) on the initial conditions, the population transfer and the relative energy is revealed, and the stationary, periodical and chaotic MQSTs are found. Finally, we illustrate that the relative population oscillation can undergo a process from order to chaos, through a series of period-doubling bifurcations.