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Stability of Affine Difference Equation

If the absolute value of Stability of Affine Difference Equation is less than 1 ( Stability of Affine Difference Equation or Stability of Affine Difference Equation ), the long run solution will be equal to the equilibrium value. We called the equilibrium value is attracting or stable. Regardless the choice of Stability of Affine Difference Equation , the solution of a stable difference equation will stabilize itself even if it is temporarily perturbed from its course.

Even if the absolute value of Stability of Affine Difference Equation is not less than 1 ( Stability of Affine Difference Equation or Stability of Affine Difference Equation ), the long run solution may be equal to the equilibrium if the value of Stability of Affine Difference Equation is chosen properly to get a constant solution (i.e. Stability of Affine Difference Equation ). This equilibrium value is unstable or repelling because any deviation, however slight, will prevent the solution from returning to its equilibrium value. For Stability of Affine Difference Equation , if Stability of Affine Difference Equation the solution will never be a constant (no equilibrium value, go without bound) and if Stability of Affine Difference Equation then the solution is always a constant. In this later case the equilibrium is unstable (repelling) because if the solution is perturbed, it remains at its perturbed value and does not return to its original value.

See also: Application in Personal Finance

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Preferable reference for this tutorial is

Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\