Dynamics of a higher order rational difference equation

Abstract

Abstract. In this paper, we will investigate the nonlinear rational di§erence equation Our concentration is on invariant intervals, periodic character, the character of semicycles and global asymptotic stability of all positive solutions of equation(1). xn+1 = xn + xnk Bxn + Cxnk ; n = 0; 1; ::: It is worth to mention that our results solve the open problem proposed by Kulenvic and L Copy DYNAMICS OF A k thorder RATIONAL DIFFERENCE EQUATION M. SALEH, S. ABUBAHAA Abstract. In this paper, we will investigate the nonlinear rational di§erence equation Our concentration is on invariant intervals, periodic character, the character of semicycles and global asymptotic stability of all positive solutions of equation(1). xn+1 = xn + xnk Bxn + Cxnk ; n = 0; 1; ::: It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Di§erence Equations: with Open Problems and Conjectures