Dynamical Systems as Models for Long Term Behavior

Dynamical systems, also known as systems of ordinary differential equations, form the backbone of the mathematical sciences -- physical, biological, or social. They have been formed into spectacular tools for short-term predictions of natural systems. But they generally cannot predict long-term behavior  reliably. This fact -- well-known to dynamical systems theorists in the pure math community -- seems unknown to many practitioners in the modeling community. The math behind this fact is known as bifurcation theory, and more information may be found in my MS#127, The Misuse of Mathematics, at the bottom of my article list (click the title of this blog).