标题:
差分方程Xn+1=axn+bX2n/(cxn+dn-1)的解性质的研究Studying of Property of the Solution of the Nonlinear Difference EquationXn+1=axn+bX2n/(cxn+dn-1)
作者:
颜丽敏, 许晓婕, 刘静
关键字:
有理性差分方程, 渐进稳定性, 全局吸引性Rational Difference Equation; Asymptotical Stability; Global Attractivity
期刊名称:
《Pure Mathematics》, Vol.1 No.3, 2011-10-31
摘要:
文献[1]中研究了差分方程Xn+1=axn+bX2n/(cxn+dn-1)的解性质的研究，(a,b,c,d是正实数)解的有界性、平衡点的局部及全局吸引性，并给出了其几类特殊情形下的解的表达式。本文首先指出文献[1]中的第2、3段的讨论方法是不正确的。然后本文中我们对平衡点的性质进行了讨论，分为两种情况进行研究，分别为 (1-a )(c+d)≠ b及(1-a )(c+d)= b 。在第一种情况中可以得到平衡解在适当的条件下是全局吸引的，在第二种情况下得到任意实数都是平衡解且是不渐进稳定的。在每种情况中举了一些数值例子，并用相应的软件画出其图像，从而进一步证明了结论的正确性。
In paper [1], some properties are investigated about
difference equation Xn+1=axn+bX2n/(cxn+dn-1)
Studying of Property of the Solution of the Nonlinear Difference EquationXn+1=axn+bX2n/(cxn+dn-1)，where a>0,b>0,c>0,d>0, and the initial conditions x1,x 0∈（0，+∞）such as the
boundedness of the solution and the properties of the equilibrium point. In
this paper we will prove that some methods used in paper [1] are wrong at
first. Then we continue to study some properties of the difference equation
under dif-ferent circumstances. We get some interesting conclusions. At last,
we use some numerical examples to verify the conclusions that we get in this
paper.