Document Type
Article
Date of Original Version
2009
Abstract
For nonnegative real numbers, a, β, y, A, B, and C such that B + C > 0 and a + β + y > 0, the difference equation xn+1 = (a + βxn + yxn-1), n = 0, 1, 2, … has a unique positive equilibrium. A proof is given here for the following statements: (1) For every choice of positive paramenters a, β, y, A, B, and C, all solutions to the difference equation xn+1 = (a, βxn, yxn-1)/(A + Bxn + Cxn-1), n = 0, 1, 2, … x-1, x0 ∈ (0, ∞) converge to the positive equilibrium or to a prime period-two solution. (2) For every choice of positive parameters a, β, y, B, and C, all solutions to the difference equation xn+1 = (a, xn + yxn-1)/(Bxn + Cxn-1), n = 0, 1, 2, …, x-1, x0 ∈ (0,∞) converge to the positive equilibrium or to a prime period-two solution.
Citation/Publisher Attribution
Basu, S., & Merino, O. (2009). Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations. Advances in Difference Equations, 2009, Article ID: 128602. doi: 10.1155/2009/128602
Available at: https://doi.org/10.1155/2009/128602
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.