Numerical Schemes for Exploring Delayed Nonlinear Feedback

摘要

We propose to use characteristic exponents of averaged instability for diagnostics of complex systems. It is shown that these exponents can be calculated from eigenvalues of the product matrix obtained from Jacobian-matrixes of the multi-step transformation. The effective scheme for calculating the product matrix in a finite time interval is developed, it allows to reduce calculation complexity (about by an order) due to exact factorization of the Jacobian-matrix in restricted time intervals. The detailed analytical analysis of the reconstruction process is implemented with respect to delay nonlinear equations for both Runge - Kutta and Euler approaches.