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.

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