Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization
The joint analysis of several signals is essential for better understanding of the principles underlying the complex systems dynamics. We consider three methods for estimating the stability of the relative dynamics of two surrogate processes. The first one is based on calculation of the phase synchr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | Russian |
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Saint Petersburg Electrotechnical University "LETI"
2017-12-01
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| Series: | Известия высших учебных заведений России: Радиоэлектроника |
| Subjects: | |
| Online Access: | https://re.eltech.ru/jour/article/view/199 |
| _version_ | 1797874515226656768 |
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| author | S. A. Pyko N. S. Pyko O. A. Markelov Yu. D. Uljanitski M. I. Bogachev |
| author_facet | S. A. Pyko N. S. Pyko O. A. Markelov Yu. D. Uljanitski M. I. Bogachev |
| author_sort | S. A. Pyko |
| collection | DOAJ |
| description | The joint analysis of several signals is essential for better understanding of the principles underlying the complex systems dynamics. We consider three methods for estimating the stability of the relative dynamics of two surrogate processes. The first one is based on calculation of the phase synchronization coefficient S and the second one on estimation of the cross-conditional entropy CE. The third approach uses the average value of the coherence function of the two processes - the coherence coefficient C. We study the sensitivity of these methods in relation to the amplitude randomization between test processes. All methods are applied to analyze two types of normally distributed random stochastic processes, with either short-term correlations characterized by finite correlation time or long-term correlations with theoretically infinite correlation time characterized by Hurst exponents. In our research, we generate two copies of the surrogate process with either short-term or long-term correlations. Then we attribute the additive white noise to one of these copies at first with the uniform distribution and then with the Gaussian distribution and the same variance. Next, we calculate the coefficients that characterize the mutual behavior of the two test processes and estimate their statistical characteristics. It is found that the sensitivity of all methods to Gaussian additive noise is higher than that of uniform one. We show that processes with long-term correlation react more actively to the additive amplitude noise then processes with short-term correlation. The influence of Hurst exponent value for the processes with long-term correlation is expressed for the coefficients S and C. The influence of correlation time is demonstrated for the coefficients S and СЕ. Our results may be useful in investigations of the mutual dynamics of two processes belonging to the considered types. |
| first_indexed | 2024-04-10T01:33:17Z |
| format | Article |
| id | doaj.art-05857d1260734f6cb6bd179c1095acdc |
| institution | Directory Open Access Journal |
| issn | 1993-8985 2658-4794 |
| language | Russian |
| last_indexed | 2024-04-10T01:33:17Z |
| publishDate | 2017-12-01 |
| publisher | Saint Petersburg Electrotechnical University "LETI" |
| record_format | Article |
| series | Известия высших учебных заведений России: Радиоэлектроника |
| spelling | doaj.art-05857d1260734f6cb6bd179c1095acdc2023-03-13T09:20:22ZrusSaint Petersburg Electrotechnical University "LETI"Известия высших учебных заведений России: Радиоэлектроника1993-89852658-47942017-12-01062127198Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude RandomizationS. A. Pyko0N. S. Pyko1O. A. Markelov2Yu. D. Uljanitski3M. I. Bogachev4Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)The joint analysis of several signals is essential for better understanding of the principles underlying the complex systems dynamics. We consider three methods for estimating the stability of the relative dynamics of two surrogate processes. The first one is based on calculation of the phase synchronization coefficient S and the second one on estimation of the cross-conditional entropy CE. The third approach uses the average value of the coherence function of the two processes - the coherence coefficient C. We study the sensitivity of these methods in relation to the amplitude randomization between test processes. All methods are applied to analyze two types of normally distributed random stochastic processes, with either short-term correlations characterized by finite correlation time or long-term correlations with theoretically infinite correlation time characterized by Hurst exponents. In our research, we generate two copies of the surrogate process with either short-term or long-term correlations. Then we attribute the additive white noise to one of these copies at first with the uniform distribution and then with the Gaussian distribution and the same variance. Next, we calculate the coefficients that characterize the mutual behavior of the two test processes and estimate their statistical characteristics. It is found that the sensitivity of all methods to Gaussian additive noise is higher than that of uniform one. We show that processes with long-term correlation react more actively to the additive amplitude noise then processes with short-term correlation. The influence of Hurst exponent value for the processes with long-term correlation is expressed for the coefficients S and C. The influence of correlation time is demonstrated for the coefficients S and СЕ. Our results may be useful in investigations of the mutual dynamics of two processes belonging to the considered types.https://re.eltech.ru/jour/article/view/199коэффициент фазовой синхронизациивремя корреляциипоказатель херстафункция когерентностиотносительная условная энтропия |
| spellingShingle | S. A. Pyko N. S. Pyko O. A. Markelov Yu. D. Uljanitski M. I. Bogachev Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization Известия высших учебных заведений России: Радиоэлектроника коэффициент фазовой синхронизации время корреляции показатель херста функция когерентности относительная условная энтропия |
| title | Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization |
| title_full | Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization |
| title_fullStr | Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization |
| title_full_unstemmed | Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization |
| title_short | Investigation of Mutual Behavior of Stochastic Normally Distributed Processes with Additive Amplitude Randomization |
| title_sort | investigation of mutual behavior of stochastic normally distributed processes with additive amplitude randomization |
| topic | коэффициент фазовой синхронизации время корреляции показатель херста функция когерентности относительная условная энтропия |
| url | https://re.eltech.ru/jour/article/view/199 |
| work_keys_str_mv | AT sapyko investigationofmutualbehaviorofstochasticnormallydistributedprocesseswithadditiveamplituderandomization AT nspyko investigationofmutualbehaviorofstochasticnormallydistributedprocesseswithadditiveamplituderandomization AT oamarkelov investigationofmutualbehaviorofstochasticnormallydistributedprocesseswithadditiveamplituderandomization AT yuduljanitski investigationofmutualbehaviorofstochasticnormallydistributedprocesseswithadditiveamplituderandomization AT mibogachev investigationofmutualbehaviorofstochasticnormallydistributedprocesseswithadditiveamplituderandomization |