Stability of Hyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation. (21st April 2015) - Atawna, S.; Abu-Saris, R.; Ismail, E. S.; Hashim, I.
Abstract : Our goal in this paper is to investigate the global asymptotic stability of the hyperbolic equilibrium solution of the second order rational difference equation x n + 1 = α + β x n + γ x n - 1 / A + B x n + C x n - 1, n = 0, 1, 2, …, where the parameters A ≥ 0 and B, C, α, β, γ are positive real numbers and the initial conditions x - 1, x 0 are nonnegative real numbers such that A + B x 0 + C x - 1 > 0 . In particular, we solve Conjecture 5.201.1 proposed by Camouzis and Ladas in their book (2008) which appeared previously in Conjecture 11.4.2 in Kulenović and Ladas monograph (2002).