  We investigate the chaotic behavior of a circular test string in the Lifshitz
spacetimes considering the critical exponent $z$ as an external control
parameter. It is demonstrated that two primary tools to observe chaos in this
system are Poincar\'{e} section and Lyapunov exponent. Finally, the numerical
result shows that if $z=1$, the string dynamics is regular, while in a case
slightly larger than $z=1$, the dynamics can be irregular and chaotic.
