  We study the transient behavior of damage propagation in the two-dimensional
spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis
dynamics. We find that, for a particular region in the second-order transition
regime of the crystal field--temperature phase diagram of the model, the
average Hamming distance decreases exponentially with time in the weakly
damaged system. Additionally, its rate of decay appears to depend linearly on a
number of Hamiltonian parameters, namely the crystal field, temperature,
applied magnetic field, but also on the amount of damage. Finally, a
comparative study using Metropolis and Glauber dynamics indicates a slower
decay rate of the average Hamming distance for the Glauber protocol.
