  The holographic complexity has been studied in a background which includes a
critical point in the dual field theory. We have examined how the complexity
rate and the saturation time of dynamical variables in the theory behave as one
moves towards the critical point. Two significant results of our analysis are
that (i) it takes more time for the complexity in field theory dual to become
time dependent as one moves away from the critical point and (ii) near the
critical point the complexity starts evolving linearly in time sooner than the
other points away from it. We also observe different behaviour for complexity
rate in action and volume prescriptions. In action prescription we have used
the time scales in theory to obtain the dynamical critical exponent and
interestingly have observed that different time scales produce the same value
up to very small error.
