STATISTICAL METHODS FOR EVALUATING THE CONNECTIVITY OF DYNAMIC SYSTEMS BASED ON A SEPARATE TIME PROJECTION

Abstract

Based on the approaches of nonlinear dynamics to the estimation of invariants of a dynamical
system, the possibility of determining the degree of coupling of various dynamical systems is
considered. The dynamic coupling of the studied systems is understood as the number of common
components in the systems that determine the time evolution of the observed projections. The proposed
method has been tested on model dynamic systems and used to analyze the behavior of complex
dynamic systems observed in geophysics – apparent electrical resistance in two orthogonal
directions and relative vertical surface displacements. The data of long regime observations used
in the calculations in the seismically active region are interesting by the available facts of sensitivity
to the stress-strain state of the geophysical medium. Assuming a parameter of the state of the
medium as a common component of the observed dynamic processes of various nature, the number
of common components of the systems is estimated based on the proposed methodology. The paper
proposes a statistical method for finding individual samples of synchronous changes in variations
of the dynamic parameters of the observed number of geophysical fields. Assuming the unsteady
nature of the formation of a dynamic system in the presence of a large number of acting external
factors, it is relevant to determine the time intervals for synchronizing the properties of dynamic
systems when a dominant effect appears. The result of the application of the developed method is
the conclusion about synchronization of variations in the correlation dimension of volumetric
deformation at different time scales in the phase of the occurrence of strong seismic events.