Existence of a Period-Two Solution in Linearizable Difference Equations

Authors

E. J. Janowski, University of Rhode Island
Mustafa RS Kulenović, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

10-8-2013

Abstract

Consider the difference equation x_n+1 = f(x_n, …, x_n-k), n = 0, 1, …, where l, k ∈ {1, 2, . . .} and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation x_n+l = Σ^k_{i = 1–l} g_ix_n-1, n = 0, 1, . . . , where l, k ∈ {1, 2, . . .} and the functions g_i : ℝ^k+l → ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution when l = 1.

Citation/Publisher Attribution

E. J. Janowski and M. R. S. Kulenović, “Existence of a Period-Two Solution in Linearizable Difference Equations,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 421545, 9 pages, 2013. doi:10.1155/2013/421545

Available at: http://dx.doi.org/10.1155/2013/421545

Creative Commons License

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