11: Nonlinear Differential Equations
Reference: Strogatz, Sections 2.2, 2.4, 3.1, 3.2, 3.4, 6.3, 6.4, 8.2
We now turn our attention to nonlinear differential equations. In particular, we study how small changes in the parameters of a system can result in qualitative changes in the dynamics. These qualitative changes in the dynamics are called bifurcations. To understand bifurcations, we first need to understand the concepts of fixed points and stability.