Identifying the sensitive parameter(s) in a system of equations is not so much difficult as not often considered during the problem solving process.
As the term implies, the degree to which a parameter is sensitive will be visible by the effect it’s values have on the simulation. It is analogous to the effect of a single observation on an overfit model in statistics.
However, unlike statistics, the sensitive parameter may not be the most *important* parameter. Statistical models tend to give an estimate of the relative importance of a factor (at least linear/nonlinear models). However, the model may be sensitive to the synthesis or degradation rate of a protein, but clearly this is a small part of the conceptual system. So we should not assume sensitivity means importance.
Sensitivity of a parameter is important when estimating parameter values. If a parameter estimation greatly changes the simulation, an algorithm may have great difficulty optimizing the entire parameter set. I will discuss a solution to this problem in a post on iterative curve fitting.