Article
MSC:
34C99,
39A10,
39A20,
39A22,
39A23,
39A30,
39A99,
65Q10 | MR 2683642 | Zbl 1224.39015 | DOI: 10.21136/MB.2010.140707
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Keywords:
difference equation; boundedness; period two solution; convergence; global stability
difference equation; boundedness; period two solution; convergence; global stability
Summary:
The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation $$ x_{n+1}=\frac {\alpha _0x_n+\alpha _1x_{n-l}+\alpha _2x_{n-k}} {\beta _0x_n+\beta _1x_{n-l}+\beta _2x_{n-k}}, \quad n=0,1,2,\dots $$ where the coefficients $\alpha _i,\beta _i\in (0,\infty )$ for $ i=0,1,2,$ and $l$, $k$ are positive integers. The initial conditions $ x_{-k}, \dots , x_{-l}, \dots , x_{-1}, x_0 $ are arbitrary positive real numbers such that $l<k$. Some numerical experiments are presented.
References:
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