Abstract
The correlation method for operative detection of recurrent states in complex dynamical systems at irregular measurements was proposed. The concepts of correlation for the case of the vectors of states of the trajectory of dynamics of complex systems and estimates of vectors correlation for a fixed length fragment moving along the trajectory were generalized. The space with scalar product of states vectors is used to implement the method. Estimation of the magnitudes of correlations of state vectors makes it possible to interpret them as corresponding levels of energy interaction of states vectors and to detect degree of their recurrence. In this case, calculation of the magnitudes of correlation are carried out only based on the known measurements of the state vector and does not require determining the threshold and the method of distance calculation, traditionally used in the methods of recurrent plots. The efficiency of the proposed method was tested on a specific example of experimental data of the actual dynamics of the vector of states of pollution of the urban atmosphere. The following gas pollutants were considered as components of the vector of state: formaldehyde, ammonia and carbon dioxide. The obtained results in general indicate the efficiency of the proposed method. It was established experimentally that the correlation method in case of irregular measurements of atmospheric contaminations ensures the authenticity of detection of recurrent states, corresponding to maximum correlation of states. In this case, the correlation assessment should be conducted for a movable fragment of a trajectory of the states vector. The length of the fragment should not be more than 10 responses
Highlights
Most actual objects of natural and artificial origin are complex non-linear dynamic systems
A constructive tool for studying the recurrence of states of complex dynamic systems is the methods of recurrent plots (RP) [2]
Objective complexity and uncertainty of dynamic systems, as well as the need for authentic display of the recurrent states of systems create the problem of improving the known methods for detection of recurrent states in complex dynamic systems
Summary
Most actual objects of natural and artificial origin are complex non-linear dynamic systems. A constructive tool for studying the recurrence of states of complex dynamic systems is the methods of recurrent plots (RP) [2]. These methods belong to the visual class and are the basis of modern methods for recurrent quantitative assessment (RQA) of states. The capabilities of the well-known RQA methods depend significantly on the authenticity of displaying recurrent states using the visual methods of the RP. Objective complexity and uncertainty of dynamic systems, as well as the need for authentic display of the recurrent states of systems create the problem of improving the known methods for detection of recurrent states in complex dynamic systems
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