Nonlinear chemical dynamics is the study of oscillations, waves, fronts, patterns, and chaos in chemical systems away from equilibrium. An important tool in this field is the use of numerical simulations. We introduce numerical integration for simple chemical rate expressions and examine the limitations to standard methods, illustrating the erroneous results that can be obtained for simple coupled differential equations using two algorithms in Mathcad. We demonstrate phase plane analysis in a simple driven pendulum and the time delay method for reconstructing the systems attractor. We apply the technique to several important systems, including the Lotka-Volterra model, the Brusselator, and the Oregonator. This document contains an extensive bibliography for oscillating reactions.

An attractor with a fixed point.