MatCont is developed
under the supervision of
W. Govaerts
(Gent,B) and Yu.A. Kuznetsov (Utrecht,NL)
with contributions by
O. De Feo (Lausanne,CH),
A. Dhooge (Gent,B), V. Govorukhin (Rostov,RU), R. Khoshsiar Ghaziani (Gent,B) H.G.E. Meijer (Utrecht,NL),
W. Mestrom (Utrecht,NL), A. Riet (Utrecht,NL) and B.
Sautois (Gent,B).
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 of MatCont and Cl_MatCont
is to provide a continuation and bifurcation 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 dynamical systems.
It is developed in parallel with the command line continuation toolbox
Cl_MatCont.
The package (Cl_)MatCont is freely available for noncommercial
use on an as is basis. It should never be sold as part of some other
software product. Also, in no circumstances can the authors be held
liable for any deficiency, fault or other mishappening with regard to the
use or performance of (Cl_)MatCont.
The following actions are
supported by the present version of MatCont and Cl_MatCont:

continuation of equilibrium and
periodic solutions with respect to a control parameter;

computation of phase response
curves and their derivatives for periodic solutions;

detection of fold, Hopf and branching
points on curves of equilibria;

computation of normal form coefficients
for fold and Hopf equilibrium bifurcations;

continuation of fold and Hopf
equilibrium bifurcations in two control parameters;

detection of all codim 2 equilibrium
bifurcations (cusp, BogdanovTakens, generalized Hopf, zeroHopf, and double
Hopf) on fold and Hopf curves;

computation of normal form coefficients
for all codim 2 equilibrium bifurcations;

detection of branch bifurcation
points on fold curves;

continuation of branching equilibria
in three control parameters;

detection of flip, fold, torus
and branch bifurcations of periodic solutions;

computation of normal form coefficients
for bifurcations of periodic solutions;

continuation of flip, fold and
torus bifurcations of periodic solutions in two control parameters;

detection of several codim 2
bifurcations of periodic solutions on fold, flip and torus bifurcation
curves;

switching to the period doubled
branch in a flip point;

branch switching at branch points
of equilibria and limit cycles;

continuation of branching periodic
solutions in three control parameters;

continuation of orbits homoclinic
to a hyperbolic saddle;

continuation of orbits homoclinic
to a saddlenode.
MatCont :

makes the Matlab ODEsuite for
time integration interactively available;

can use the Matlab Symbolic Toolbox
for computing derivatives whenever it is installed.

maintains archive of computed
curves;

user functions can be added;

online help function is implemented;

Jacobian matrices of defining
functions for periodic orbits and their bifurcations are programed
as Ccodes which are compiled using the Matlab builtin compiler to increase
speed.
The following actions are supported by
the present version of Cl_MatCont_for_maps:

continuation of fixed points of maps and
iterates of maps with respect to a control parameter;

detection of fold, flip, NeimarkSacker and branch
points on curves of fixed points;

computation of normal form coefficients for fold, flip and
NeimarkSacker bifurcations;

continuation of fold, flip and NeimarkSacker bifurcations in two
control parameters;

detection of all eleven codim 2 fixed point bifurcations on curves of fold,
flip and NeimarkSacker bifurcations;

computation of normal form coefficients for all codim 2 bifurcations of fixed
points;

switching to the period doubled branch in a flip point;

branch switching at branch points of fixed points;

switching to branches of codim 1 bifurcations rooted in codim 2 points.
