文章基本信息

标题：Complete Asymptotic and Bifurcation Analysis for a Difference Equation with Piecewise Constant Control
本地全文：下载
作者：Chengmin Hou ; Lili Han ; SuiSun Cheng 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2010
卷号：2010
期号：1
页码：542073
DOI：10.1155/2010/542073
语种：English
出版社：Hindawi Publishing Corporation
摘要：We consider a difference equation involving three parameters and a piecewise constant control function with an additional positive threshold . Treating the threshold as a bifurcation parameter that varies between 0 and , we work out a complete asymptotic and bifurcation analysis. Among other things, we show that all solutions either tend to a limit 1-cycle or to a limit 2-cycle and, we find the exact regions of attraction for these cycles depending on the size of the threshold. In particular, we show that when the threshold is either small or large, there is only one corresponding limit 1-cycle which is globally attractive. It is hoped that the results obtained here will be useful in understanding interacting network models involving piecewise constant control functions.
关键词：Difference Equation ; Global Attractor ; Bifurcation Analysis ; Bifurcation Parameter ; Continuity Argument