We discuss the new GUI environment of the MATLAB software package MatCont for numerical bifurcation studies of continuous dynamical systems. It is built upon the corresponding command line package Cl_MatCont. The package is freely available via sourceforge.net/matcont and offers both interfaces. Mathematically, the functionalities of MatCont with respect to bifurcation techniques are unrivalled. For instance, no other software allows to compute the normal forms of codimension two bifurcations of periodic orbits, or to start curves of codimension one bifurcations of periodic orbits from codimension two equilibrium points. Though widely used, the previous version of MatCont was at the end of its life span of maintainability and the new MatCont gives it a fresh start. It is completely reorganized with a better documentation and an improved data handling with a Data Browser, a Diagram Organizer and a Spreadsheet Viewer. Other new features are the Command Line Interface, the functionality of computing Poincaré maps and many facilities to simplify the use of the software. As an application we discuss a computational model that describes the stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long interstimulus intervals. Unlike previous studies we incorporate the time that the stimulus is on (Ton) and off (Toff) explicitly as bifurcation parameters of the model. We compute the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the region of bistability of repeating and alternating behavior is a wedge in the parameter plane bounded by two curves of limit point bifurcations of periodic orbits and one curve of period-doubling bifurcations.