As far as I know, the concept of stiffness is hard to define rigorously, but there are plenty of handwavy descriptions and motivating examples in the literature when it comes to linear differential equations. At the same time I have never seen an explicit and straightforward definition of a stiff nonlinear differential equation. That being said, I feel like there should be one, and I just haven't seen it yet. To outline, my questions are:
Is there such thing as stiff nonlinear differential equation? If so, how is it defined?
The most straightforward approach to define one is to use linearization, but I am not sure if this is a good idea as the accuracy of linearization will probably have an decisive impact on the region of absolute stability.