一类四阶有理差分方程的振动规律和全局稳定性  

Rules of Oscillation and Global Asymptotic Stability for a Fourth-Order Rational Difference Equation

作　　者：陈云新[1] 

机构地区：[1]南华大学数理学院,中国衡阳421001

出　　处：《湖南师范大学自然科学学报》2009年第4期14-17,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10771094);湖南省教育厅科研重点资助项目(09A080)

摘　　要：主要讨论了一类四阶有理差分方程xn+1=(xn-2+xn-3)/(xn-2xn-3+1),n=0,1,2,…,初始值x-3,x-2,x-1,x0∈(0,∞)的振动规律和全局稳定性,即描述了其解的振动周期为15,且正、负半环长的规律为:4+,3-,1+,2-,2+,1-,1+,1-;又指出了解之间存在xn+kΔ(C(xn+k))x(nC(xn+k)C(xn))(n≥-3)的大小关系;并得到了方程的平衡点是全局渐近稳定的.A fourth-order rational difference equation is considered. The rules of oscillation and global asymptotic stability is described clearly. Mainly, the lengths of positive and negative semi-cycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4^＋ ,3^- ,1^＋ ,2^- ,2^＋ ,1^- ,1^＋ ,1^- in a period. The relation between solution and solution is xn＋kΔ （C （xn＋k ） ）xn^（C（xn＋k）C（xn）） （n ≥ -3 ）. By utilizing this rule and relation, its negative equilibrium point is verified to be globally asymptotically stable.

关 键 词：有理差分方程 振动规律 全局渐近稳定 

分 类 号：O175.7[理学—数学]