The development of matrix decomposition theory for nonlinear analysis of chaotic attractors of complex systems and signals

A new method of nonlinear analysis of chaotic attractors on the basis of the proposed matrix decomposition theory of vector functions in state space of complex systems is developed. It includes an analysis of linear term of the matrix series as well as an estimation of influence of quadratic term (in generally, high order terms) of the matrix series on stability of complex system. Using results of the matrix decomposition high order Lyapunov characteristic exponents are defined.