Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

Authors

M. Garić-Demirović
Mustafa RS Kulenović, University of Rhode IslandFollow
N. Nurkanović

Document Type

Article

Date of Original Version

10-1-2013

Abstract

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x_n+1 = x²_n-1/(ax²_n + bx_nx_n-1 + cx²_n-1), n = 0, 1, 2, …, where the parameters a, b, and c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable.

Citation/Publisher Attribution

M. Garić-Demirović, M. R. S. Kulenović, and M. Nurkanović, “Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation,” The Scientific World Journal, vol. 2013, Article ID 210846, 10 pages, 2013. doi:10.1155/2013/210846

Available at: http://dx.doi.org/10.1155/2013/210846

Creative Commons License

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