Application of expansion into matrix series to analysis of attractors of complex nonlinear dynamical systems

Decomposition methods of nonlinear operators describing the behavior of system in state space (phase space) are very important for analysis, identification and modeling of nonlinear dynamical systems (NDS), in particular NDS with self-organization (or complex NDS). The aim of this paper is derivation and classification of matrix series describing decomposition of vector functions from phase space variables and NDS operators into state space. This paper also develops some statements of matrix decomposition and main principles for analysis of attractors of complex NDS.