Global stability in a non-autonomous discrete growth system (Q1823183)

A simple model of population growth under density dependent selection is considered which leads to a discrete model of type \(\Delta x=a_ t(x- \hat x_ 1)(x-\hat x_ 2)\) with time dependent coefficient \(a_ t\) and fixed points \(\hat x_ 1\) and \(\hat x_ 2\). The qualitative behaviour of solutions of this model is discussed and it is shown, that under certain assumptions the well-known behaviour of the corresponding autonomous system will carry over to the non-autonomous case. Thus, results on global stability can be obtained in the latter system, too.