Asymptotic properties of the positive equilibrium of a discrete survival model

摘要

This paper is concerned with the discrete Wazewska and Lasota model (*)xn+1−xn=−μxn+pe−νxn−k,where μ∈(0,1), ν,p∈(0,∞) and k∈{0,1,2…}. We show that every positive solution of (*) is persistent, and then we provide sufficient conditions for oscillation of all solutions about x∗. Finally, we give sufficient conditions for x∗ to be stable or attractive.