The assumptions abound. Of course, these assumptions taken into account, this sort of modeling is almost useless. Keep in mind that if this linear modeling models a system that is actually linear, the model approximates the reality, often fairly well. The possibility of nonlinearity is not even considered. In the early 1900 s, Henri Poincar developed a new kind of mathematics now called topology .
Topology provides a new way of analyzing dynamical systems.
Using what is called a Poincar section, along with some other high-powered mathematics, we can visualize the behavior of dynamical systems in an entirely new sense. However, I will mention the strange attractor . Loosely, an attractor is what a function eventually settles down to. Any other attractor is as strange attractor. Strange attractors are extremely complex, and they describe extremely complex behavior.