The study of differential equations requires good and powerful mathematical software. Also, a flexible and extendible package is important. A powerful and widely used environment for scientific computing is MATLAB. The aim ofMatCont and Cl_MatCont is to provide a continuation toolbox which is compatible with the standard MATLAB ODE representation of differential equations.

MatCont is a graphical MATLAB package for the interactive numerical study of a range of parameterized nonlinear problems. The current version is freely available at http://www.matcont.UGent.be where also a slightly more general non–GUI version Cl_MatCont is available.

The following functions are supported by the present version of MatCont :

• continuation of equilibrium and periodic solutions with respect to a control parameter;
• detection of fold, Hopf and branching points on curves of equilibria;
• normal form analysis of fold and Hopf equilibrium bifurcations;
• continuation of fold and Hopf equilibrium bifurcations in two control parameters;
• detection of all codim 2 equilibrium bifurcations (cusp, Bogdanov-Takens, generalized Hopf, zero-Hopf, and double Hopf) on fold and Hopf curves;
• detection of branch bifurcation points on fold curves;
• continuation of branch points of equilibria in three control parameters;
• detection of flip, fold, torus and branch bifurcations of periodic solutions;
• continuation of flip, fold and torus bifurcations of periodic solutions in two control parameters;
• continuation of the period doubled branch in a flip point;
• continuation of branch bifurcations of periodic solutions in three control parameters;
• makes the MATLAB odesuite for time integration interactively available;
• can use the MATLAB Symbolic Toolbox for computing derivatives whenever it is installed.
• the archive filter limits the number of curves of a particular type;
• branch switching at branch points of equilibria and limit cycles;
• user functions can be added;
• computation of normal form coefficients for bifurcations of periodic solutions;
• detection of several codim 2 bifurcations on fold, flip and torus bifurcation curves;
• help function.