Analysis of periodicity for a new class of non-linear difference equations by using a new method. (English) Zbl 1438.39013
Summary: This paper aims to investigate the periodicity of solutions of the following delay nonlinear difference equation \[ x_{n+1}=ax_{n-k}+bx_{n-l}+\frac{\sum^{k}_{i=0}a_{i}x_{n-i}}{\sum^{l}_{j=0} b_{j}x_{n-j}}, n=0, 1, \ldots \] where the parameters \(a, b, a_0, \ldots, a_k, b_0, b_1, \ldots, b_l\) are non-zero real numbers, \(k, l \in \mathbb{Z}^+\) and the initial values \(x_{-\max\{k,\ell\}}, \ldots, x_{-1}, x_0\in\mathbb{R}-\{0\}\). Moreover, several numerical simulations are provided to support obtained results.
MSC:
| 39A23 | Periodic solutions of difference equations |
| 39A20 | Multiplicative and other generalized difference equations |
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