Rate Equations

Abstract

We provide a brief introduction to applications of ordinary differential equation (ODE) rate equations in chemistry, biology and physics. In mechanics, Newton’s laws prescribe how to write the rate equations while in other fields, the ODEs are based on different principles. In the context of chemical reactions, the law of mass action yields systems of first-order ODEs in terms of the reactants and products. For population dynamics and epidemic models, similar considerations yield comparable nonlinear ODEs. We review geometric and analytic considerations based on local properties for single first-order autonomous equations (phase line dynamics) and extend them to the qualitative understanding of global behaviour in two-dimensional phase plane systems.