Basins of attraction of equilibrium and boundary points of second-order difference equations

We investigate the global behaviour of the difference equation of the form with (Formula presented)non-negative parameters and initial conditions such that B \u3e 0, b + d + e + f \u3e 0. We give a precise description of the basins of attraction of different equilibrium points, and show that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium points or non-hyperbolic equilibrium points are in fact the global stable manifolds of neighbouring saddle or non-hyperbolic equilibrium points. Different types of bifurcations when one or more parameters b; d; e; f are 0 are explained