Lyapunov exponents for complex systems with delayed feedback

Analytical and numerical analysis is implemented for two methods of Lyapunov exponents calculation. The first is based on successive multiplication of functional matrixes corresponding to discrete transformations and calculation of eigenvalues for the obtained matrix. The second approach is based on successive orthogonalization of multiplied matrixes using QR-decomposition. The analytical model for describing functional maps of discrete iterations derived from delay differential equation is proposed, which implements representation of the product matrix through matrixes of canonical form that reduces calculation complexity.