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Affine Dynamical System

The difference equation Difference Equation Tutorial; Affine Dynamcal System is called affine dynamical system. It is one of the simplest forms of linear 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

Difference Equation Tutorial; Affine Dynamcal System

Equation ( 1 )

Solution

Difference Equation Tutorial; Affine Dynamcal System

Equation ( 2 )

Equilibrium

Difference Equation Tutorial; Affine Dynamcal System

Equation ( 3 )

Stability

Stable if and only if Difference Equation Tutorial; Affine Dynamcal System

Unstable if other cases (i.e. Difference Equation Tutorial; Affine Dynamcal System or Difference Equation Tutorial; Affine Dynamcal System )

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 Also: Numerical Example

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Preferable reference for this tutorial is

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