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Affine Difference Equation

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The difference equation  is called affine dynamical system. It is one of the simplest forms of difference equation. It has characteristic of first order linear discrete dynamical system with constant coefficient and constant input to the system. Table below shows the equation, solution, equilibrium value and stability of such system.

Difference equation

Equation (1)

Solution

Equation (2)

Equilibrium

Equation (3)

Stability

Stable if and only if

Unstable if other cases (i.e.  or )

Equation (4)

Notice that the solution depends on both the difference equation and the initial condition. Derivation of the solution and equilibrium are shown in previous pages.

See: Numerical Example

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