Abstract
Researchers widely use methods for calculation of recurrence plots based on measurement of dynamics of a vector of states in a phase space for visual and quantitative analysis of the behavior of complex dynamic systems in various fields. Such methods have high potential capabilities. However, one cannot use them directly for the operative calculation of recurrence plots at the real speed of measurements of a vector of states, taking into account irregularity of measurements. One of the reasons is the lack of a method, which would be capable of operative and reliable mapping of recurrence states of real systems in recurrence plots at irregular measurements of a vector of states.We propose a method for the operative calculation of recurrence plots at irregular measurements. Its base is a scientific analysis of reasons for low reliability and impossibility of an operative calculation of recurrence plots, as well as search and substantiation of constructive methods for their elimination. Such methods include: current calculation of recurrence plots; improvement of a phase space by introduction of an operation of scalar product for vectors of states; adaptation of a recurrence threshold to measurement results. The base of a process of the current calculation of recurrence plots is a use of only current and previous measurements of a vector of states of the system. It is possible to reconcile two key factors of low reliability of mapping of recurrence states in diagrams related to uncertainty of a norm and a threshold of recurrence in the proposed improved phase space.The above has made possible to propose a threshold adaptation method for conical regions of recurrence. It has been proposed to use two adaptive thresholds with different angular parameters of recurrence cones in the calculation to ensure reliable mapping of recurrence states in diagrams under conditions of irregular measurement of a vector of states. We confirmed the operability of the proposed operative method for calculation of recurrence plots and illustrated it by an example with irregular measurements of the real dynamics of a vector of states of dangerous pollution in the urban atmosphere
Highlights
The study of most complex systems, both natural and artificial, shows that their bases are non-linear processes, and their behavior satisfies a fundamental principle of dissipative dynamical systems, that is state recurrence
We propose a method for the RP calculation based on the difference of two RPs to expand advantages of application of an adaptive threshold at irregular measurements
A method has been developed for the operative RP calculation at irregular measurements of a vector of states of real dynamic systems
Summary
The study of most complex systems, both natural and artificial, shows that their bases are non-linear processes, and their behavior satisfies a fundamental principle of dissipative dynamical systems, that is state recurrence. Mathematics and cybernetics – applied aspects plots (RP) proposed in [2] to visualize recurrence states of complex dynamic systems, RP methods are fundamental for quantitative state recurrence analysis (RQA). Capabilities of RQA methods depend substantially on reliability of mapping of the recurrent behavior of real systems in RP. It is known that the reliability of mapping of recurrence states in RP depends substantially on conditions and nature of obtaining of measurement information. The threshold uncertainty of the methods limits reliability of mapping of recurrence states significantly under unknown and changing conditions, which are characteristic to most applications. In this regard, the problem of improvement of methods for calculation of RP arises
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
