Basin of Attraction through Invariant Curves and Dominant Functions

Abstract EN

We study a second-order difference equation of the form zn+1=znF(zn-1)+h, where both F(z) and zF(z) are decreasing.

We consider a set of invariant curves at h=1 and use it to characterize the behaviour of solutions when h>1 and when 0

The case h>1 is related to the Y2K problem.

For 0

In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria.