A global behavior of the positive solutions of $ x_{n+1}=\dfrac{ \beta x_n +x_{n-2}}{A+Bx_n +x_{n-2}}$

Commun. Korean Math. Soc. 2008 Vol. 23, No. 1, 61-65 Printed March 1, 2008

JongAn Park Department of Mathematics, Kangwon National University, Chuncheon 200-701, Korea

Abstract : In this paper we prove that every positive solution of the third order rational difference equation $$ x_{n+1}=\dfrac{ \beta x_n +x_{n-2}}{A+Bx_n +x_{n-2}} $$ converges to the positive equilibrium point $$ \overline{x}=\dfrac{\beta+1-A}{B+1}, $$ where $ 0

Keywords : difference equations, equilibrium point