Symmetric bifurcation theory has a rich history with many beautiful theoretical results, and also see, in particular for maps. In many case studies, the form of the model allows an analytical exploration of the effect of symmetry. Meanwhile, the development of numerical tools to study bifurcations with symmetry is limited. There has been much more progress in numerical approaches for generic dynamical systems. There is a special version MatcontM that is devoted to maps. This toolbox supports numerical continuation and bifurcation analysis of fixed points and cycles of iterated maps. MatcontM detects limit point, period doubling and Neimark-Sacker points and supports continuation of these bifurcations in two control parameters. Along such bifurcation curves, all codimension ? bifurcations are also detected. The critical normal form coefficients of codim ? and codim ? bifurcations are computed as developed. These coefficients are needed to verify non-degeneracy and to determine the corresponding bifurcation scenario. In the presence of symmetries, certain generic conditions in the analysis are no longer satisfied. Therefore, we studied how to adapt MatcontM in the case of symmetries. Here we report on a case study of a symmetric bifurcation in maps. In particular, we focus on algorithms and changes in the toolbox MatcontM needed to support the bifurcation analysis in a numerical context. کلیدواژه فارسی کلیدواژه انگلیسی
