Java Applets for Visualizing Vector Fields of ODEs

Below are useful applets for visualizing the vector fields of dynamical systems:

Vector field of an ODE
Phase plane of a 2D system

Phase Portraits

A dynamical system can be modeled as a system of coupled differential equations u' = Au. The solutions to any such system are described by the eigenvalues and the eigen-vectors of A Depending on the eigenvalues, the phase portrait of a 2-dimensional system falls into one of the 10 classes in the handout below:

Phase portraits of 2 dimensional dynamical systems