Global Asymptotic Stability in a Rational Equation*

Abstract

Abstract In this paper, a sufficient condition is obtained for the global asymptotic stability of the following rational difference equation where a \in [0, \infty ) and the initial values x_{-1}, \hspace{0.167em} x_{0} \in (0, \infty ). Keywords: Rational difference equationGlobal asymptotic stabilitySemicycleEquilibrium point39A10 Notes ‡[e-mail] Project by NNSF of China (grant: 10071022), Mathematical Tianyuan Foundation of China (grant: TY10026002-01-05-03), and Shanghai Priority Academic Discipline.