Is there a way to delineate the parameter of highest influence in a system of differential equations?

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So I have a system of nonlinear ordinary differential equations dependent on parameters. These equations can traditionally be solved numerically with robust methods and the solution is well defined.

Although the latter satisfies me, I was curious if there was a method, perhaps computationally, to figure out which parameter influences the model the most. I understand this can be defined in many ways, and I am happy with any way of quantification.