T.S.Krasnopolskaya, Ye.D.Pechuk Modeling the dynamic system from the output signal data |
Acoustic bulletin, Vol. 13 ¹ 4, (2010) |
| The paper deals with comparing of two main methods for deriving (reconstruction) of the evolution equations of the dynamic systems from their output signals. These are the method of successive differentiation and the delay method. For the first time, the linear interval of dependence of the divergence of reconstructed system versus the delay parameter has been used to determine the optimal value of the delay. The reconstruction of the dynamic system describing the planar physical pendulum oscillation after its output signal has been presented as an example. The obtained results are the evidence of the possibility to reconstitute the regular and chaotic motions of the pendulum with the allowance for the nonlinearities up to the six order inclusively in the right-hand sides of equations of the reconstructed systems. The spectral techniques, phase portrait mapping and Lyapunov exponents were used in this study. |
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KEY WORDS: non-linear dynamic systems, regular regimes, dynamic chaos, phase portret, the Lyapunov exponent |
| TEXT LANGUAGE: Russian |