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

Abstract

We investigate the global behaviour of the difference equation of the form

with non-negative parameters and initial conditions such that . 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 are 0 are explained.

Keywords::

• attractivity
• basin
• difference equation
• invariant manifolds
• stable manifold

MSC (2010) Classification::

• 39A10
• 39A11