Basins of attraction of equilibrium and boundary points of second-order difference equations
Date of Original Version
We investigate the global behaviour of the difference equation of the form with (Formula presented)non-negative parameters and initial conditions such that B > 0, b + d + e + f > 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.
Journal of Difference Equations and Applications
Jašarević, S., and M. R.S. Kulenović. "Basins of attraction of equilibrium and boundary points of second-order difference equations." Journal of Difference Equations and Applications 20, 5 (2014): 947-959. doi:10.1080/10236198.2013.855733.