Date of Original Version
We investigate the global character of the difference equation of the form
xn+1 = f (xn, xn–1), n = 0,1, . . .
with several period-two solutions, where f is increasing in all its variables. We show that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium solutions or period-two solutions are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium solutions or period-two solutions. As an application of our results we give the global dynamics of three feasible models in population dynamics which includes the nonlinearity of Beverton-Holt and sigmoid Beverton-Holt types.
MSC: 39A10; 39A20; 37B25; 37D10
Keywords: attractivity; basin; difference equation; invariant manifolds; period-two solutions
Bilgin, A., Kulenovic, M. R. S., and Pilav, E. (2016). Basins of attraction of period-two solutions of monotone difference equations. Advances in Difference Equations, 74. doi: 10.1186/s13662-016-0801-y
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