Global asymptotic stability of a second order rational difference equation
Hu, Lin-Xia; Li, Wan-Tong; Stević, Stevo; Hu, Lin-Xia; Department of Mathematics, Tianshui Normal University; , ; School of Mathematics and Statistics, Lanzhou University; Li, Wan-Tong; School of Mathematics and Statistics, Lanzhou University; Stević, Stevo; Mathematical Institute of the Serbian Academy of Science
Журнал:
Journal of Difference Equations and Applications
Дата:
2008
Аннотация:
The main goal of the paper is to confirm Conjecture 9.5.5 stated by Kulenović and Ladas in Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures (Chapman & Hall/CRC, Boca Raton, FL, 2002). The boundedness, invariant intervals, semicycles and global attractivity of all nonnegative solutions of the equationare studied, where the parameters and the initial conditions are such that . It is shown that if the equation has no prime period-two solutions, then the unique positive equilibrium of the equation is globally asymptotically stable.
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