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.