Dynamic behavior of a nonlinear rational difference equation and generalization

作者：Shi Qihong^*; Xiao Qian; Yuan Guoqiang; Liu Xiaojun

来源：Advances in Difference Equations, 2011, 2011(1): 36.

DOI：10.1186/1687-1847-2011-36

• Nonlinear
• Difference equation
• Global stability
• Positive solution

This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x (n) = (x (n-k) + x (n-m) + x (n-l) )/(x (n-k) x (n-m) + x (n-m) x (n-l) +1) with the initial data {x(-l),x(-l+1),...,x(-1)}is an element of R-+(l) and 1 a parts per thousand currency sign k a parts per thousand currency sign m a parts per thousand currency sign l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004) to a large extent. In addition, some propositions for generalized equations are reported.

• 出版日期2011