  We study the motion of a ring string in the background of the Bardeen-AdS
black hole surrounded by the quintessence dark energy. The effects of the
magnetic monopole charge, the quintessence state parameter, and the
quintessence normalization parameter on the dynamical behavior of the ring
string are respectively analyzed. Our numerical results show that the chaotic
behavior of string generally becomes stronger with the increase of the
quintessence normalization parameter. In particular, the conditions for the
existence of chaos are distinctly diverse for two different quintessence state
parameters. Furthermore, it is found that the magnetic charge does not
significantly affect the chaotic behavior of the string in a specific range.
