The study of differential equations requires good and powerful mathematical software. Also, a flexible and extendible package is important. However, most of the existing software all have their own manner of specifying the system or are written in a relatively low-level programming language, so it is hard to extend it.
A powerful and widely used environment for scientific computing is matlab [12]. The aim of MatCont and CL_MatCont is to provide a continuation toolbox which is compatible with the standard matlab ODE representation of differential equations. The user can easily use his/her models without rewriting them to a specific package. The matlab programming language makes the use and extensions of the toolbox very easy.
This document is structured as follows. In section 2 the underlying mathematics of continuation will be treated. Section 3 introduces how singularities will be represented. The toolbox software specification is explained in section 4 with more details on the GUI or Graphical User Interface in section 5. A more complex application of the toolbox, continuation of equilibria, is described in section 6. Section 7 describes the continuation of limit cycles and the computation of the phase response curve. Section 8 describes the continuation of codim 1 bifurcations, at present limit points of equilibria, Hopf bifurcation points of equilibria, period doubling bifurcation points of limit cycles, fold bifurcation points of limit cycles and Neimark-Sacker bifurcation points of limit cycles. Section 9 describes the continuation of codim 2 bifurcations, at present branch points of equilibria and branch points of limit cycles. Section 10 deals with the continuation of homoclinic orbits.