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Zbl 1085.39006
Dehghan, Mehdi; Jaberi Douraki, Majid; Jaberi Douraki, Marjan
Dynamics of a rational difference equation using both theoretical and computational approaches.
(English)
[J] Appl. Math. Comput. 168, No. 2, 756-775 (2005). ISSN 0096-3003

The authors study the global behavior of the difference equation $x_n+1=(p+ x_{n}) (x_{n}+ qx_{n-k})^{-1},\ k \in \{1,2,\dots\}$, where the initial conditions $x_k,x_k+1,\dots,x_0$ are non-negative and the parameters $p$ and $q$ are also non-negative. They investigate the oscillatory character, invariant intervals, the boundedness and the global stability of the solutions of the above equation. The analysis of semi cycles is verified under some specific conditions posed on the coefficients. Finally, the authors give some numerical examples to support their theoretical discussions.
[Hussain A. El-Saify (Beni Suef)]
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations
65Q05 Numerical methods for functional equations

Keywords: local asymptotic stability; invariant interval; semi cycle behavior; global asymptotic stability; boundedness; oscillation; numerical examples

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