Dynamics of a higher-order rational difference equation

Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

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.  

Global Dynamics for a Higher Order Rational Difference Equation

In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...

Dynamics of a System of Rational Higher-Order Difference Equation

Dynamics and behavior of a higher order rational difference equation

We study the global result, boundedness, and periodicity of solutions of the difference equation xn+1 = a+ bxn−l + cxn−k dxn−l + exn−k , n = 0, 1, . . . , where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x−t, x−t+1, . . . , x−1 and x0 are positive real numbers where t = max{l, k}, l 6= k. c ©2016 All rights reserved.