chapter  3
50 Pages


As we’ve seen in Chapter 2, the dynamics of vector fields on the line is very limited: all solutions either settle down to equilibrium or head out to od. Given the triviality of the dynamics, what’s interesting about one-dimensional systems? Answer: Dependence on parameters. The qualitative structure of the flow can change as parameters are varied. In particular, fixed points can be created or destroyed, or their stability can change. These qualitative changes in the dynamics are called bifurcations, and the parameter values at which they occur are called bifurcation points.