Chaotic dynamic methods based on decomposition of vector functions in vector-matrix series into state-space

Decomposition methods of nonlinear operators describing the behavior of systems in state-space (phase-space) are important for the analysis, identification and modeling of nonlinear dynamic systems (NDSs), in particular NDSs with self-organization (or complex systems). In connection with this the aim of this paper is the deduction and classification of vector-matrix series describing the decomposition of vector functions from phase-space variables, shift operators trajectories of nonlinear differential equations and NDS operators in state-space.