Ergodic behavior of locally regulated branching populations

摘要: For a class of processes modeling the evolution spatially structured population with migration and logistic local regulation reproduction dynamics we show convergence towards an upper invariant measure from suitable initial distributions. It follows recent work A. Etheridge that this is non-trivial for sufficiently large super-criticality in reproduction. small prove extinction by comparison mean field model. This latter result extends also to more general regulations.