| 10
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The ten possible types of solutions to affine difference equation
are sorted in the table below.
| No |
Type
of Solution |
|
Cases |
| 1. |
Constant |
|
,
|
|
,
|
|
,
|
|
,
|
|
,
|
|
,
|
| 2. |
Linearly
increasing without bound |
|
,
|
| 3. |
Linearly
decreasing without bound |
|
,
|
| 4. |
Exponentially
increasing without bound |
|
,
|
| 5. |
Exponentially
decreasing without bound |
|
,
|
| 6. |
Exponentially
increasing to a bound |
|
,
|
| 7. |
Exponentially
decreasing to a bound |
|
,
|
| 8. |
Oscillating
with constant amplitude |
|
,
|
|
,
|
| 9. |
Oscillating
with increasing amplitude |
|
,
|
|
,
|
| 10. |
Oscillating
with decreasing amplitude |
|
,
|
|
,
|
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|