A note on a rational difference equation

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

On a Conjecture for a Higher-Order Rational Difference Equation

studying the behavior of solutions of a second-order rational difference equation and a rational system

in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

A period 5 difference equation

The main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

Global stability of a rational difference equation

We consider the higher-order nonlinear difference equation xn 1 p qxn−k / 1 xn rxn−k , n 0, 1, . . . with the parameters, and the initial conditions x−k, . . . , x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open probl...