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21. 5. 2014.
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 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.