Equilibrium of Difference Equation

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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 to be equal to equilibrium value .

Example

Find equilibrium value of difference equation

Solution:

Write the difference equation in the form gives

Equate produces or .

Example

Find the equilibrium values of difference equation

Solution

Equate and solve the quadratic equation produces and .

See: Numerical example

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Preferable reference for this tutorial is

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