The following provides a simple example for computing the steady-state give a simple mathematical model.
Consider the open chemical system composed of two reactions with rates and :
We will assume that the chemical species  and  are fixed external species and  is an internal chemical species that is allowed to change. The fixed boundaries is to ensure the system can reach a steady-state. If we assume simple irreversible mass-action kinetics, the differential equation describing the concentration of  is given by:
To find the steady-state the differential equation is set to zero and the equation rearranged to solve for 
This is the steady-state concentration of .
The stability of this system can be determined by making a perturbation  in  This can be expressed as:
Note that the  will elicit a change in the rate of change. 
At steady-state , therefore the rate of change of  as a result of this perturbation is:
This shows that the perturbation,  decays exponetially, hence the system is stable.