高阶非线性差分方程的全局吸引性Global attractivity of a higher order nonlinear difference equation
唐国梅;
摘要(Abstract):
研究了一类高阶非线性差分方程所有正解的周期性,不变区间及全局吸引性.证明了方程的正平衡点是在一个依赖于参数的盆里的全局吸引子.
关键词(KeyWords): 差分方程;不变区间;素二周期解;全局吸引子
基金项目(Foundation):
作者(Authors): 唐国梅;
参考文献(References):
- [1]Li W T,Sun H R.Dynamics of a rational difference equation[J].Appl.Math.Comput.,2005,163:577-591.
- [2]deVault R,Kosmala W,Ladas G,et al.Global behavior of yn+1=(p+ynffk)/(qyn+ynffk)[J].Nonlin.Anal.TMA,2001,47:4743-4751.
- [3]Kuruklis S A.The asymptotic stability of xn+1ffaxn+bxnffk=0[J].J.Math.Anal.Appl.,1994,188:719-731.
- [4]Kocic V L,Ladas G.Global Behavior of Nonlinear Difference Equations of Higher Order with Applications[M].Dordrecht:Kluwer Academic,1993.
- [5]Cunningham K C,Kulenovic M R S,Ladas G,et al.On the recursive sequence xn+1=(α+βxn)/(Bxn+Cxnff1)[J].Nonlinear Anal.TMA,2001,47:4603-4614.
- [6]Agarwal R P,Li W T,Pang P Y H.Asymptotic behavior of a class of nonlinear delay difference equations[J].J.Diff.Equat.Appl.,2002,8:719-728.
- [7]Dehghan M,Rastegar N.On the global behavior of a high-order rational difference equation[J].Comput.Phys.Commun.,2009,180:873-878.
- [8]Kosmala W,Kulenovic M R S,Ladas G,et al.On the rational sequence yn+1=(p+ynff1)/(qyn+ynff1)[J].J.Math.Anal.Appl.,2000,251:571-586.
- [9]Kulenovic M R S,Ladas G,Prokup N R.A rational difference equation[J].Comput.Math.Appl.,2001,41:671-678.
- [10]Kulenovic M R S,Ladas G,Prokup N R.On the recursive sequence xn+1=(αxn+βxn-1)/(1+xn)[J].J.Diff.Equat.Appl.,2000,6:563-576.
- [11]Kulenovic M R S,Ladas G.Dynamics of Second Order Rational Difference Equations with Open Problemsand Conjectures[M].Boca Raton:Chapman and Hall/CRC,2002.
- [12]Kulenovic M R S,Merino O.Global attractivity of the equilibrium of xn+1=(pxn+xn-1)/(qxn+xn-1)for q
- [13]Hu L X,Li W T,Stevic S.Global asymptotic stability of a second order rational difference equation[J].J.Diff.Equ.Appl.,2008,14(8):779-797.
- [14]Yan X X,Li W T,Zhao Z.Global asymptotic stability for a higher order nonlinear rational differenceequations[J].Appl.Math.Comput.,2006,182:1819-1831.
- [15]Su Y H,Li W T.Global behavior of a higher order nonlinear rational difference equation[J].J.Diff.Equat.Appl.,2005,11(10):947-958.