DEVELOPMENT OF A SELF-ADJUSTING METHOD FOR CALCULATING RECURRENT DIAGRAMS IN A SPACE WITH A SCALAR PRODUCT

Abstract

A self-adjusting method for calculating recurrence diagrams has been developed. The proposed method is aimed at overcoming the metric-threshold uncertainty inherent in the known methods for calculating recurrence diagrams. The method provides invariance to the nature of the measured data, and also allows to display the recurrence of states, adequate to real systems of various fields. A new scientific result consists in the theoretical justification of the method for calculating recurrence diagrams, which is capable of overcoming the existing metric-threshold uncertainty of known methods on the basis of self-adjusting by measurements by improving the topology of the metric space. The topology is improved due to the additional introduction of the scalar product of state vectors into the operation space. This allowed to develop a self-adjusting method for calculating recurrence diagrams with increased accuracy and adequacy of the display of recurrence states of real systems. Moreover, the method has a relatively low computational complexity, providing invariance with respect to the nature of the irregularity of measurements.