Open AccessDynamics of a Rational Difference Equation
Author(s) -
Xin Jia,
Lin-Xia Hu,
Wan–Tong Li
Publication year - 2010
Publication title -
advances in difference equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.67
H-Index - 51
eISSN - 1687-1847
pISSN - 1687-1839
DOI - 10.1155/2010/970720
Subject(s) - mathematics , partial differential equation , ordinary differential equation , invariant (physics) , differential equation , integer (computer science) , work (physics) , dynamics (music) , mathematical analysis , physics , acoustics , mechanical engineering , computer science , engineering , mathematical physics , programming language
The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n∈ℕ0, where the parameters α,β,γ∈[0,∞), k≥2 is an integer, and the initial conditions x-k,…,x0∈[0,∞). It is shown that the unique positive equilibrium of the equation is globally asymptotically stable under the condition β≤1. The result partially solves the open problem proposed by Kulenović and Ladas in work (2002)