Slavov lab | Quantitative Biology
Seeking  principles
in the coordination among protein synthesis, metabolism, cell growth and differentiation

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