Modelling Non-Equilibrium Systems with Equations

In this chapter we will return our attention to the phenomenological approach in which some macroscopic variables are chosen to represent the state of the system. The system evolves according to some coupled differential equations (usually nonlinear). While models represented by such coupled equations are commonplace in the physical sciences (e.g. the double pendulum, BZ reaction etc), as we shall see, they are useful also in the biological (e.g. epidemiology) and social sciences. The models studied here are not only relatively simple but can be quantitatively tested.