Dynamics and behaviors of a third-order system of 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.  

Dynamics of the Third Order Lyness’ Difference Equation

This paper studies the iterates of the third order Lyness’ recurrence xk+3 = (a + xk+1 + xk+2)/xk, with positive initial conditions, being a also a positive parameter. It is known that for a = 1 all the sequences generated by this recurrence are 8-periodic. We prove that for each a 6= 1 there are infinitely many initial conditions giving rise to periodic sequences which have almost all the even...

Dynamics of a System of Rational Higher-Order 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.

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...