Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

Authors

Senada Kalabušić
Mustafa RS Kulenović, University of Rhode IslandFollow
M. Mehuljić

Document Type

Article

Date of Original Version

4-27-2014

Abstract

We investigate the local stability and the global asymptotic stability of the difference equation x_n+1 = (αx²_n + βx_n x_n-1 + yx_n−1) / (Ax²_n + Bx_nx_n-1 + Cx_n-1), n = 0, 1, …. with nonnegative parameters and initial conditions such that Ax²_n + Bxnx_n-1 + Cx_n-1 > 0, for all n ≥ 0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β = B = 0, in which case we show that such equation exhibits a global period doubling bifurcation.

Citation/Publisher Attribution

Senada Kalabušić, M. R. S. Kulenović, and M. Mehuljić, “Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 920410, 13 pages, 2014. doi:10.1155/2014/920410

Available at: http://dx.doi.org/10.1155/2014/920410

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.