On the difference equation \(x_n = \frac{p+x_{n-2}}{qx_{n-t}+x_{n-s}}\) (Q2381397)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the difference equation \(x_n = \frac{p+x_{n-2}}{qx_{n-t}+x_{n-s}}\) |
scientific article |
Statements
On the difference equation \(x_n = \frac{p+x_{n-2}}{qx_{n-t}+x_{n-s}}\) (English)
0 references
17 September 2007
0 references
For the difference equation in the title with positire coefficients it is proved that the positive solutions are persistent. The equilibrium is a global attractor of all positive solutions, if \(p\geq q\) or \(p<q\leq 1+4p\). In the case \(p=q\) all positive solutions converge to 1.
0 references
rational difference equation
0 references
persistence
0 references
equilibrium
0 references
global attractivity
0 references
positive solutions
0 references
0 references
0 references
