16 July 2002 Diagnostics of a complex delayed system by numerical approaches
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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 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.
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Victor F. Dailyudenko, Victor F. Dailyudenko, } "Diagnostics of a complex delayed system by numerical approaches", Proc. SPIE 4733, Component and Systems Diagnostics, Prognostics, and Health Management II, (16 July 2002); doi: 10.1117/12.475508; https://doi.org/10.1117/12.475508

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