何万生,胡林霞,李万同

• 1:天水师范学院数学系
• 2:天水师范学院数学系
• 3:兰州大学数学系 天水741001
• 4:天水741001

摘要(Abstract)：

研究了差分方程 xn+1 =a - bxn- k A - xn( a≥ 0 ,A≥ b≥ 0 )的全局稳定性和正解的周期性质 .证明了方程的一个正平衡点是一个全局吸引子 ,并给出了相应的吸引域

关键词(KeyWords)： 差分方程;全局稳定性;吸引性;正解

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金资助项目 ( 10 1710 40 )

作者(Author): 何万生,胡林霞,李万同

参考文献(References)：

• [1]　OuC H,TangH S,L uoW.Global stability for a class of difference equation[J].Appl.Math.J.ChinesUniv.Ser.B,2000,15(1):33～36.
• [2]　GibbonsC H,KulenovicM R S,L adsG.On the recuresive sequence yn+1=((α+βyn-1)/(γ+yn))[J].Math.Sci.Res.,Hot-L ine,2000,4(2):1～11.
• [3]　YanX X,L iW T.Global attractivity in the recursive sequence xn+1=(α-βxn)/(γ- xn-1))[J].ApplMath.Comput.,2003,138:415～423.
• [4]　AboutalebM T,EI-SayedM A,HamzaA E.Stability of the recursive sequence xn+1=(α-βxn)/(γ+xn-1)[J].J.Math.Anal.Appl.,2001,261:126～133.
• [5]　CunninghamK C,KulenovicM R S,L adasG,ValicentiS V.On the recursive sequence xn=(α+βxn)/(Bxn+Cxn-1)[J].NonlinearAnalysisTMA,2001,47:4603～4614.
• [6]　KulenovicM R S,L adasG,ProkupN R.On the recursive sequence xn+1=(αxn+βxn-1)/(1+xn)[J].J.Difer.EquationAppl,2000,5:563～576.
• [7]　KocicV L,L adasG.GlobalBehavior ofNonlinearDifferenceEquations ofHigherOrder withApplica-tion[M].Dordrecht,KluwerAcademicPublishers,1993.
• [8]　KuruklisS A.The asymptotic stability of xn+1- axn+bxn-k=0[J].J.Math.Anal.Appl.,1994,188:719～731.
• [9]　DevaultR,KosmalaW,L adasG,SchultzS W.Global behavior of yn+1=(p+yn-k)/(qyn+yn-k)[J].NonlinearAnalysisTAM,2001,47:4743～4751.
• [10]　L iW T,SunH R.Global attractivity in a rational recursive[J].Dysterms andApplication,2002,11(3):339～345.
• [11]　YanX X,L iW T,SunH R.Global attractivity in a higher order nonlinear difference equation[J].Ap-pl.Math.,E-Notes,2002,2:51～58.
• [12]　GibbonsC H,KulenovicM R S,L adasG,VoulovH D.On the trichotomy character of xn+1=(α+βxn+γxn-1)/(A+xn)[J].J.DifferenceEquations and applications,2002,8(1):75～92.
• [13]　KocicV L ,L adasG.Global attractivity in a second- order nonlinear difference equation[J].J.Math.Anal.Appl.,1993,180:144～150.
• [14]　HeW S,L iW T,YanX X.GlobalAttractivity in aNonlinearDifferenceEquation[J].InternationalJournal ofAppliedMathematics,2002,11(3):283～293.
• [15]　HeW S,LiW T,YanX X.GlobalAttractivity ofDifferenceEquationxn+1=α+(xn-k/xn)[J].Appl.Math.Comput.,in press