on the global asymptotic stability for a rational recursive sequence

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation

Global asymptotic stability of a nonlinear recursive sequence

In this work, we investigate the global asymptotic stability of the following nonlinear recursive sequence: x n+1 = x n x b n−2 + x b n−3 + x b n−1 + a x n x b n−3 + x b n−2 + x b n−1 + a (1) where a, b ∈ [0, ∞) and the initial values x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers.

On the Rational Recursive Sequence

Our main objective is to study some qualitative behavior of the solutions of the difference equation xn+1 = γxn−k + (axn + bxn−k) / (cxn − dxn−k) , n = 0, 1, 2, ..., where the initial conditions x−k,..., x−1, x0 are arbitrary positive real numbers and the coefficients γ, a, b, c and d are positive constants, while k is a positive integer number.

On a (2,2)-rational Recursive Sequence

We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+ βyn)/(1 + yn−1) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a+ byn)/(A+Byn−1), when th...

Global asymptotic stability of a higher order rational difference equation

In this note, we consider the following rational difference equation: xn+1 = f (xn−r1 , . . . , xn−rk )g(xn−m1 , . . . , xn−ml )+ 1 f (xn−r1 , . . . , xn−rk )+ g(xn−m1 , . . . , xn−ml ) , n= 0,1, . . . , where f ∈ C((0,+∞)k, (0,+∞)) and g ∈ C((0,+∞)l, (0,+∞)) with k, l ∈ {1,2, . . .}, 0 r1 < · · ·< rk and 0 m1 < · · ·<ml , and the initial values are positive real numbers. We give sufficient con...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})