Reconstruction of self-oscillating systems with delay time modulation
The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in...
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| Format: | Article |
| Language: | English |
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Saratov State University
2025-01-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/01/and_2025-1_ponomarenko-prokhorov_27-37.pdf |
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| author | Ponomarenko, Vladimir Ivanovich Prokhorov, Mihail Dmitrievich |
| author_facet | Ponomarenko, Vladimir Ivanovich Prokhorov, Mihail Dmitrievich |
| author_sort | Ponomarenko, Vladimir Ivanovich |
| collection | DOAJ |
| description | The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series. |
| format | Article |
| id | doaj-art-7324fef2e7854f3793cbbc28666bc8eb |
| institution | Kabale University |
| issn | 0869-6632 2542-1905 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj-art-7324fef2e7854f3793cbbc28666bc8eb2025-01-31T04:17:11ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052025-01-01331273710.18500/0869-6632-003131Reconstruction of self-oscillating systems with delay time modulationPonomarenko, Vladimir Ivanovich0Prokhorov, Mihail Dmitrievich1Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences, ul. Zelyonaya, 38, Saratov, 410019, RussiaSaratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences, ul. Zelyonaya, 38, Saratov, 410019, RussiaThe aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series. https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/01/and_2025-1_ponomarenko-prokhorov_27-37.pdfsystems with delay time modulationlaminar chaosreconstruction of systems from time seriesstatistics of extrema |
| spellingShingle | Ponomarenko, Vladimir Ivanovich Prokhorov, Mihail Dmitrievich Reconstruction of self-oscillating systems with delay time modulation Известия высших учебных заведений: Прикладная нелинейная динамика systems with delay time modulation laminar chaos reconstruction of systems from time series statistics of extrema |
| title | Reconstruction of self-oscillating systems with delay time modulation |
| title_full | Reconstruction of self-oscillating systems with delay time modulation |
| title_fullStr | Reconstruction of self-oscillating systems with delay time modulation |
| title_full_unstemmed | Reconstruction of self-oscillating systems with delay time modulation |
| title_short | Reconstruction of self-oscillating systems with delay time modulation |
| title_sort | reconstruction of self oscillating systems with delay time modulation |
| topic | systems with delay time modulation laminar chaos reconstruction of systems from time series statistics of extrema |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/01/and_2025-1_ponomarenko-prokhorov_27-37.pdf |
| work_keys_str_mv | AT ponomarenkovladimirivanovich reconstructionofselfoscillatingsystemswithdelaytimemodulation AT prokhorovmihaildmitrievich reconstructionofselfoscillatingsystemswithdelaytimemodulation |