Are there bushes in a forest?
The authors study a Markov process, whose state space consists of the configurations on \({\mathbb{Z}}^ d\), where each site is in one of the three states 0, 1 and 2 resp. grass, bush, tree. They assume, that 1's and 2's die (i.e. become 0) at rate 1 and produce offsprings at rate \(\lambda_ 1\) resp. \(\lambda_ 2\), which replace the state at a position of a certain neighbourhood with equal probability, if this site is in a lower state. Sufficient conditions are given both for the case, that 1's die out as for the case of permanent coexistence of 1's and 2's.
scientific article; zbMATH DE number 4190892