| 一类三阶有理差分方程的奇点集和解的渐近性 |
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| 引用本文： | 全卫贞.一类三阶有理差分方程的奇点集和解的渐近性[J].数学的实践与认识,2017(1):229-235. |
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| 作者姓名： | 全卫贞 |
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| 作者单位： | 岭南师范学院基础教育学院,广东湛江,524037 |
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| 摘 要： | 研究三阶有理差分方程x_(n+1)=ax_(n-1)+x_(n-1)x_n/bx_(n-2)+cx_n,n=0,1,2,...的奇点集和解{x_n}_(n=-2)~∞的渐近性,其中a,b,c∈R,初始值x_(-2),x_(-1),x_0∈R.由a,b,c的取值的不同,而得到解的不同的渐近性.
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| 关 键 词： | 差分方程 Riccati差分方程 奇点集 周期解 渐近性 |
The Forbidden Set and the Asymptotic Behaviour of Solutions for a Three-order Rational Difference Equation |
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| Abstract: | We study the forbidden set and asymptotic behaviour of solutions of the threeorder difference equation xn+1 =axn-1 + xn-1xn/bxn-2+cxn,n =0,1,2,… With a,b,c ∈ R and initial valuas x-2,x-1,x0 ∈ R.By the value of a,b,c is different,and obtain the different asymptotic behavior of solutions. |
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| Keywords: | difference equation riccati difference equation forbidden set periodic solution asymptotic behaviour |
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