Boundary modified contact processes (Q1582135)

The authors modify the classical one-dimensional contact process by changing the birth rate to the left and right of the cluster of existing particles to a value \(\lambda_e\) different from the value \(\lambda_i\) within the cluster. They ask the question to what extend the external birth rate influences the survival probability of the process. It is shown that if the internal birth rate \(\lambda_i\) is smaller than the critical value of the standard contact process, then the process dies out for all values of \(\lambda_e\). The same holds if the external rate \(\lambda_e\leq 1\), not matter what the internal rate is. On the other hand, if \(\lambda_e>1\), then the process survives if \(\lambda_i\) is large enough. The authors also consider a multi-dimensional version of this model.