Dimension of the phase space of a dynamic system from geophysical data |
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| Authors: | A S Cherepantsev |
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| Institution: | (1) Taganrog Institute of Technology, Southern Federal University, Taganrog, Russia |
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| Abstract: | The possibility of determining parameters of complex geophysical processes is considered in terms of nonlinear dynamics. In accordance with modern approaches in the theory of nonlinear dynamic systems, the number of independent parameters controlling the behavior of a nonlinear system can be estimated from the available time realization of only one of these parameters. Model calculations showed that the dimension of the phase space of a dynamic system can be estimated from a sample of one variable. Experimental data on variations in the apparent electric resistivity (AER) and the relative vertical movement of the surface (RVMS) in a seismically active region are analyzed and the dimension of the dynamic system determining its behavior in the phase space is estimated. The resulting estimates of the embedding dimension m = 7?8 for AER variations and m = 6 for RVMS variations possibly characterize the complexity of the dynamic system describing the given fields. The method presented in the paper is also applied to the analysis of the degree of connectivity of different dynamic systems and their parameters. By the connectivity we mean the number of independent parameters simultaneously involved in the formation of the dynamic behavior of various physical fields. The model estimates demonstrate the possibility of such an approach. It is shown that variations in the AER in perpendicular directions are described by a general system of dynamic equations, whereas dynamic systems controlling the AER field and the RVMSs are interconnected only partially. The resulting dimension m = 12 estimated for the AER-RVMS system provides an estimate for the number of common controlling parameters: n = (8 + 6)?12 = 2. The methods and results presented in the paper are applicable to the construction of models of complex geophysical processes and the development and the development of new approaches and methods of identification of prognostic characteristics for the behavior of physical fields of various origins. |
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