Introduction to mathematics of analyzing nonlinear dynamic models

Economists have done dynamics very badly, from the bastardisation of the original Harrod unstable growth model by Hicks, through to today's DSGE models which pretend that a saddle node equilibrium can be an attractor. This lecture uses basic mathematical techniques to show that "multiplier-accelerator trade cycle models" aren't models at all, and explains the basics of working out the dynamical properties of low-order (3 or below) systems of nonlinear differential equations, using the classic Lotka-Volterra predator-prey model as an example. This lecture is a prelude to exploring the dynamics of my model of Minsky's Financial Instability Hypothesis.