Group-theoretical methods for simplification of stability analysis of dynamical regimes in nonlinear systems with discrete symmetry
We present a detailed description of the group-theoretical method which has been published in 2006 by the authors. This method can frequently simplify the study of the stability of different dynamical regimes in nonlinear physical systems with discrete symmetry since it allows one to split the set of the linearized (near a considered regime) nonlinear differential equations into a number of independent subsets of small dimensions. The above method is illustrated with the case of stability analysis of some dynamical regimes in the simple octahedral structure.