Dynamics of a Rational Difference Equation

Dynamics of a rational difference equation

The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn 1 α βxn γxn−k / 1 xn−k , n ∈ N0, where the parameters α, β, γ ∈ 0,∞ , k ≥ 2 is an integer, and the initial conditions x−k, . . . , x0 ∈ 0,∞ . It is shown that the unique positive equilibrium of the equation is globally asymptotically ...

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 Rational Difference Equation

In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = Axn +Bxn−k +Cxn−l +Dxn−σ + bxn−k +hxn−l dxn−k + exn−l , n = 0,1,2, ....., where the coefficients A,B,C,D,b,d,e,h ∈ (0,∞), while k, l and σ are positive integers. The initial conditions x−σ ,...,x−l ,...,x−k, ...,x−1,x0 are arbitrary ...

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...

Dynamics of a System of Rational Higher-Order Difference Equation