On the dynamics of xn+1=δxn−2+xn−3

Abstract

We investigate the global character of solutions of the equation in the title with positive parameters and with arbitrary nonnegative initial conditions. In particular we show that every solution of the equation is bounded. We find necessary and sufficient conditions for the global asymptotic stability of the zero equilibrium. We also investigate the positive equilibrium and find regions of parameters where the positive equilibrium is a global attractor of all positive solutions.