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

Authors:
Alexander M. Krot
Affiliations:
United Institute of Informatics Problems, National Academy of Sciences of Belarus
Venue:
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Year:
2009

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Abstract

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.