SUMMARY
A method has been constructed for the threshold semi-adaptive scaling transformation. The method provides calculation of recurrent plots, which adequately map the dynamics of real complex dynamic systems in natural and technical spheres. A new scientific result implies the development of theoretical basis for the method of semi-adaptive scaling transformation of the threshold during calculation of recurrent plots by improvement of linear normalized spaces due to introduction of a scalar product of vectors. The proposed method of threshold transformation provides computation of recurrent plots with increased information content, invariance to parameters of measured state vectors, and irregularity of measurements. We performed tests of operability of the proposed method of semi-adaptive scaling transformation of the threshold based on experimental measurements of concentrations of formaldehyde, ammonia, and carbon monoxide in atmospheric air in a typical industrial city with conventional stationary and mobile sources of pollution.Taking into account the proposed method of semi-adaptive scaling transformation, the obtained results of the calculation of recurrent plots confirmed its operability in general. It was found that the calculation of RP during the semi-adaptive transformation of the threshold for various a angular dimensions of a recurrence cone, equal to 1°, 5°, 10°, and 20°, indicates that accuracy of recurrent plots in detection of dangerous states in dynamic systems increases with a decrease in angular dimensions of a cone. It was established experimentally that the values of angular dimensions of the recurrence cone should be 1–5° for adequate mapping of recurrent states of real dynamic systems with the use of calculated recurrent plots