ABSTRACT
When we descri be the beha vi our 0 f a sys tem us i ng catastrophe theory, we nearly always assume that the system stays on the equilibrium surface. This means that the speed of return to equilibrium of equations (3.1) is considered to be very fast compared to the corresponiing situation for the parameter equation (3.2). Hence th~ former equations are known as the fast equations and the latter as the slow equations. The surface of equilibrium variables is known as the slow manifold. If there is any disturbance from equil ibrium, the system is assumed to move rapidly back to equilibrium via what Zeeman (1977A) calls the 'fast foliation'. These are trajectories which are 'off' the manifold but which lead directly on to it at the same .I:!-value which held before the perturbation. If the .I:!-equations (3.2) have an equilibrium point, then the system moves more slowly on the manifold until this is reached 1 •
