  We consider the time evolution of entanglement in a finite two dimensional
transverse Ising model. The model consists of a set of 7 localized spin-1/2
particles in a two dimensional triangular lattice coupled through nearest
neighbor exchange interaction in presence of an external time dependent
magnetic field. The magnetic field is applied in different function forms:
step, exponential, hyperbolic and periodic. We found that the time evolution of
the entanglement shows an ergodic behavior under the effect of the time
dependent magnetic fields. Also we found that while the step magnetic field
causes great disturbance to the system creating rabid oscillations, the system
shows great controllability under the effect of the other magnetic fields where
the entanglement profile follows closely the shape of the applied field even
with the same frequency for periodic fields. This follow up trend breaks down
as the strength of the field, the transition constant for exponential and
hyperbolic, or frequency for periodic field increase leading to rapid
oscillations. We observed that the entanglement is very sensitive to the
initial value of the applied periodic field, the smaller the initial value the
less distorted is the entanglement profile. Furthermore, the effect of thermal
fluctuations is very devastating to the entanglement which decays very rapidly
as the temperature increases. Interestingly, although large value of the
magnetic field strength may yield small entanglement, it was found to be more
persistent against thermal fluctuations than the small field strengths.
