E. M. E. Zayed, M. A. El-Moneam, "On the Global Stability of the Nonlinear Difference Equation xn+1= α0xn+α1xn−l+α2xn−m+α3xn−k/β0xn+β1xn−l+β2xn−m+β3xn−k," WSEAS Transactions on Mathematics, vol. 11, pp. -, 2012, DOI:
E. M. E. Zayed, M. A. El-Moneam. On the Global Stability of the Nonlinear Difference Equation xn+1= α0xn+α1xn−l+α2xn−m+α3xn−k/β0xn+β1xn−l+β2xn−m+β3xn−k.
WSEAS Transactions on Mathematics. 2012;11:-.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
On the Global Stability of the Nonlinear Difference Equation xn+1= α0xn+α1xn−l+α2xn−m+α3xn−k/β0xn+β1xn−l+β2xn−m+β3xn−k
Authors: ,
Abstract: The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation <br> $$x_{n+1}= \frac{α0x_{n} + α1x_{n−l} + α2x_{n−m} + α3x_{n−k}}{β0x_{n} + β1x_{n−l} + β2x_{n−m} + β3x_{n−k}}$$, $$n = 0, 1, 2, · · ·$$ <br> where the coefficients $$α_{i}, β_{i} ∈ (0, ∞)$$ for $$i = 0, 1, 2, 3,$$ and $$l, m, k$$ are positive integers. The initial conditions $$x−k,...,x−m,...,x−l , ...,x−1, x0$$ are arbitrary positive real numbers such that $$ l < m < k$$. Some numerical experiments are presented.
Pages: - WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 11, 2012DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
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