Global Behavior of the Difference Equationxn+1=xn-1g(xn)

Global Behavior of the Difference Equation

The main objective of this paper is to study the qualitative behavior for a class of nonlinear rational difference equation. We study the local stability, periodicity, Oscillation, boundedness, and the global stability for the positive solutions of equation. Examples illustrate the importance of the results Keywords— Difference equation, stability, oscillation, boundedness, globale stability an...

Global behavior of the solutions of some difference equations

where the initial conditions x-r, x-r+1, x-r+2,..., x0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: Moreover, we obtain the form of the solution of some special cases of Equation 1 and some numerical simulations to the equation are given to illustrate our results. Let us introduce some basic definitions and some theorems tha...

Global Behavior of Two Families of Nonlinear Symmetric Difference Equations

We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević’s paper 2010 . A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili 2009 , Berenha...

Global Behavior of a Higher-order Rational Difference Equation

We investigate in this paper the global behavior of the following difference equation: xn+1 = (Pk(xn i0 ,xn i1 , . . . ,xn i2k ) + b)/(Qk(xn i0 ,xn i1 , . . . ,xn i2k ) + b), n = 0,1, . . ., under appropriate assumptions, where b [0, ), k 1, i0, i1, . . . , i2k 0,1, . . . with i0 < i1 < < i2k, the initial conditions xi 2k ,xi 2k+1, . . . ,x0 (0, ). We prove that unique equilibrium x = 1 of that...

Global behavior of a higher order difference equation