Nonlinear Systems #shorts

Nonlinear differential equations can be analyzed using linear algebra. Draw the nullclines, equilibrium points, linearlize near each equilibrium using the Jacobian then connect the dots. Examples which appear here:
Murray system, a competing species model
Volterra system, a predator pray model
Van de Pool oscillator, used to produce stable oscillators
Pendulum, a classical physical system
Double pendulum. A chaotic system on a 3 manifold
Lorentz system, a system in three dimensions.