Existence of a Period-Two Solution in Linearizable Difference Equations. (25th November 2013)

• Record Type: Journal Article
• Authors: Janowski, E. J.; Kulenović, M. R. S.
• Other Names: Kalabusic Senada Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-11-25
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/421545
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Consider the difference equation x n + 1 = f ( x n, …, x n − k ), n = 0, 1, …, where 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 = ∑ i = 1 − l k g i x n − i, 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 .