Equilibrium of Difference Equation

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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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