On the difference equation $y_{n + 1}= frac{{alpha+ y_n^p }}{{eta y_{n - 1}^p }} - frac{{gamma+ y_{n - 1}^p }}{{eta y_n^p }}$

Mathematica Slovaca

İlhan Öztürk¹  Saime Zengin¹ 

关键词: difference equations;    global stability;    period-two solutions;   

DOI  :  10.2478/s12175-011-0058-6

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, we investigate the global stability and the periodic nature of solutions of the difference equation $y_{n + 1} = frac{{alpha + y_n^p }}{{eta y_{n - 1}^p }} - frac{{gamma + y_{n - 1}^p }}{{eta y_n^p }},n = 0,1,2,...$ where α, β, γ ∈ (0,∞), α(1 − p) − γ > 0, 0 < p < 1, every y n ≠ 0 for n = −1, 0, 1, 2, … and the initial conditions y−1, y0 are arbitrary positive real numbers. We show that the equilibrium point of the difference equation is a global attractor with a basin that depends on the conditions of the coefficients.

【 授权许可】

Unknown