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Equilibrium

The equilibrium value is also called the fixed point or the critical point using phase diagram.

We can get the equilibrium points algebraically by setting Difference Equation Tutorial: Equilibrium to be equal to equilibrium value Difference Equation Tutorial: Equilibrium .

Example

Find equilibrium value of difference equation Difference Equation Tutorial: Equilibrium

Solution:

Write the difference equation in the form Difference Equation Tutorial: Equilibrium gives Difference Equation Tutorial: Equilibrium

Equate Difference Equation Tutorial: Equilibrium produces Difference Equation Tutorial: Equilibrium or Difference Equation Tutorial: Equilibrium .


Example

Find the equilibrium values of difference equation Difference Equation Tutorial: Equilibrium

Solution

Equate Difference Equation Tutorial: Equilibrium and solve the quadratic equation produces Difference Equation Tutorial: Equilibrium and Difference Equation Tutorial: Equilibrium .

See: 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\