Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.1, pp.43-51

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.1, pp.43-51

Characteristic Exponents for Vector Maps from the Product of Functional Matrices and Successive Orthogonalization of Matrix Sequence
Victor F. Dailyudenko

Estimation of averaged chaoticity for a complex system with nonlinear feedback is implemented through the spectrum of Lyapunov exponents derived from the product of functional matrices. We propose a method for calculating characteristic exponents with minimal calculation complexity using the representation of this product by the cyclic set of the permutation matrices. The results of computer experiments on calculating characteristic exponents from partially nonlinear delay differential equation confirm reliability of the proposed method. The approach with successive orthogonalization over the matrix sequence consisting of Frobenius forms is explored in detail.
Key words: characteristic exponents, nonlinear feedback, cyclic set of permutation matrices, successive orthogonalization

Full text: Acrobat PDF (213KB) PostScript (426KB) PostScript.gz (160KB)