  Magnetic skyrmions, topological spin textures observed in chiral magnets,
have attracted huge interest due to their applications in the field of
spintronics. In this work we study the stability of circular isolated skyrmions
in ferromagnetic chiral magnets under the influence of different perturbations
and external fields. To this end we develop a general systematic procedure
based in a harmonic expansion series of the skyrmion boundary which allows the
identifycation of the breakdown of the skyrmion circular shape on each
instability channel independently. We apply our approach to a few
representative spin models with actual interest in order to obtain the zero
temperature phase diagram, where isolated skyrmions emerge as metaestable
states. The results presented in this paper are in agreement with properties of
isolated skyrmions observed in recent experiments opening the possibility of
extending the analysis to more complex situations.
