Abstract
By the Poincare sections, the dynamical behaviors of the ring string in the anti-de Sitter--Gauss-Bonnet black hole are studied. A threshold value of the Gauss-Bonnet parameter $\ensuremath{\lambda}$ is found by the numerical method, below which the behavior of this dynamical system is nonchaotic and above which the behavior becomes gradually chaotic. The chaotic behavior becomes stronger with the increases of the Gauss-Bonnet parameter. It is different from the case in the anti-de Sitter--Schwarzschild black hole, which is weakly chaotic. Furthermore, we confirm our findings by the fast Lyapunov indicator.
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