  A one-dimensional branching-coalescing model is considered on a chain of
length L with reflecting boundaries. We study the phase transitions of this
model in a canonical ensemble by using the Yang-Lee description of the
non-equilibrium phase transitions. Numerical study of the canonical partition
function zeros reveals two second-order phase transitions in the system. Both
transition points are determined by the density of the particles on the chain.
In some regions the density profile of the particles has a shock structure.
