Consider a network of coupled identical or quasi-identical dynamical systems that seek to synchronize. Master stability functions are powerful mathematical tools that provide necessary and sufficient conditions for stability of the synchronous solution. Usually, a master stability function refers to a low-dimensional system whose stability is associated with that of the original high-dimensional network. Obtaining such a reduction is often quite difficult, thus can be a reason of great satisfaction for the scientist who succeeds in the task. I have worked in this area and obtained 5 different reductions in a master stability function form for different problems related to synchronization of networks. I list them below.
