Asymptotic behavior for a version of directed percolation on the honeycomb lattice

Asymptotic behavior for a generalized Domany–Kinzel model

“…The case (1) with = p p c 0 1 2 includes both the Domany-Kinzel model on the square lattice and the Domany-Kinzel model on the honeycomb lattice as bricks. The corresponding inequalities (2.13) are the same as the results we obtained in [10] and [11], but now they are valid only under the three special conditions. In the current model, we cannot get such lower bound or upper bound uniformly for any…”

“…Recently, the model has been considered in more general cases. For example, the directed percolation model on the square lattice whose vertical edges occupied with a probability p v and horizontal edges in the nth row occupied with a probability 1 if n is even and p h if n is odd [9]; the directed percolation model on the triangular lattice in terms of a square lattice with vertical probability y, horizontal probabilities 1 and x alternatively, and diagonal edges from lower-left to upper-right or from lower-right to upper-left with probability d [10]; the directed percolation model on the honeycomb lattice as bricks such that vertical edges are directed upward with probability y, and horizontal edges are directed rightward with probabilities 1 and x in alternate rows [11]. In this article, we consider a directed bond percolation on the square lattice such that horizontal edges are directed rightward with probabilities one, and vertical edges are directed upward with probabilities p 1 , p 2 alternatively in even rows and probabilities p 2 , p 1 alternatively in odd rows, as shown in figure 1.…”