On the recursive sequence \(x_{n+1} = \frac {\alpha+\beta x_{n-k+1} +\gamma x_{n-2k+1}}{Bx_{n-k+1} + Cx_{n-2k+1}}\) (Q2573569)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_{n+1} = \frac {\alpha+\beta x_{n-k+1} +\gamma x_{n-2k+1}}{Bx_{n-k+1} + Cx_{n-2k+1}}\) |
scientific article |
Statements
On the recursive sequence \(x_{n+1} = \frac {\alpha+\beta x_{n-k+1} +\gamma x_{n-2k+1}}{Bx_{n-k+1} + Cx_{n-2k+1}}\) (English)
0 references
22 November 2005
0 references
The aim of this paper is the investigation of the global asymptotic stability of all positive solutions of the nonlinear difference equation \[ x_{n+1} = \frac{\alpha + \beta x_{n-k+1}+ \gamma x_{n-2k+1}}{Bx_{n-k+1}+ Cx_{n-2k+1}} \] where all the coefficients and the initial conditions are positive and \(k = 1,2,\ldots.\) This study requires the investigation of the invariant intervals and the character of semicycles of the equation. Some numerical examples are given.
0 references
recursive sequences
0 references
global asymptotic stability
0 references
positive solutions
0 references
invariant intervals
0 references
semicycles
0 references
numerical examples
0 references
rational difference equation
0 references
0 references
0 references
