When is Nonlinear Dynamic Modeling Necessary?

The purpose of this paper is to propose an answer to the title´s question, and examine the ramifications of the provided answer. Our proposition is to quantify the nonlinearity of a system by a carefully defined 2-norm, which results from a newly constructed inner product. We develop the pertinent theory which allows the easy computation of this norm for a broad class of nonlinear dynamic systems, through Monte Carlo calculations. Explicit formulae are provided for linear systems. In addition, the problem of best approximation of a nonlinear system by a linear or nonlinear model is put in perspective, and pathways to computationally convenient solutions are charted. Practical issues are elucidated through examples of chemical engineering relevance. Further elaboration will be included in forthcoming publications.