CL MATCONTL: a continuation toolbox for large equilibrium problems in MATLAB

CL MATCONT and its GUI version MATCONT are MATLAB pack- ages for the study of dynamical systems and their bifurcations for small and moderate size problems. CL MATCONTL is an extension of the functionality of CL MATCONT to large-scale computations of equilibria bifurcations, via subspace reduction. It allows to compute curves of equi- libria, limit points, Hopf points, and branch switching. CL MATCONTL can also monitor user - deflned functions and locate their roots along com- puted curves. It can compute all necessary derivatives by flnite difierences, from flle or by using the symbolic toolbox of MATLAB. In this tutorial we describe a numerical study of a flnite difierence discretization of the 1-D Brusselator, a well known model system for au- tocatalytic chemical reactions with difiusion. Most of the capabilities of CL MATCONTL are illustrated.