Computational Dynamical Systems Using XPPAUT

Abstract

This article is written as a guide for researchers on how to employ the techniques in numerical continuation and bifurcation analysis using XPPAUT. This is a free software package to solve and analyse dynamical systems numerically. The article starts with a gentle introduction to XPPAUT, how to install this software, and an overview of the numerical routines. By using ordinary differential equations as an example, readers are guided to solve for the steady-states and also perform some graphical analysis, such as phase portraits and time-series plots. Thereafter, the sections gradually increase in complexity, covering general steps in bifurcation analysis and how to produce complete bifurcation diagrams, particularly co-dimension one and co-dimension two bifurcation plots.