Basins of Attraction of Period-Two Solutions of Monotone Difference Equations

Authors

Arzu Bilgin
Mustafa Kulenovic, University of Rhode IslandFollow
Esmir Pilav

Document Type

Article

Date of Original Version

3-14-2016

Abstract

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

x_n+1 = f (x_n, x_n–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

Citation/Publisher Attribution

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

Available at: http://dx.doi.org/10.1186/s13662-016-0801-y

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.