Dynamical phase transition of a one-dimensional transport process including death

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection alpha and death of the last particle delta. The system presents a phase transition at delta(c)(alpha), where the average position of the last particle < L > grows as root t. For delta> delta(c), a nonequilibrium stationary state exists while for delta <delta(c) the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.