  By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed
string around charged black brane with hyperscaling violation (HV). The Hawking
temperature, Lifshitz dynamical exponent and HV exponent together affect the
chaotic dynamics of this system. The temperature plays the role of driving the
closed string to escape to infinity. There is a threshold value $z_{\ast}=2$,
below which the string is captured by the black brane no matter where the
string is placed at the beginning. However, when $z>2$, the string escapes to
infinity if it is placed near the black brane at the beginning, but if the
initial position of string is far away from the black brane, it oscillates
around the black brane till eternity, which is a quasi-periodic motion. HV
exponent plays the role of driving the string falling into the black brane.
With the increase of HV exponent $\theta$, the falling velocity becomes faster.
We find that when we heat the system with large HV exponent, the chaotic system
does not essentially changes. It indicates that the HV exponent plays a very
important role in determining the state of the chaotic system. Also we study
the the effect from the winding number of the string. The study indicates that
the chaotic dynamics of the string is insensitive to the winding number.
