ANALOGY IN INTERACTIONS OF ELECTRONIC BEAMS AND HYDRODYNAMIC FLOWS WITH FIELDS OF RESONATORS AND PERIODIC STRUCTURES
Cite this article as:
Kuznetsov A. P., Kuznetsov S. P. ANALOGY IN INTERACTIONS OF ELECTRONIC BEAMS AND HYDRODYNAMIC FLOWS WITH FIELDS OF RESONATORS AND PERIODIC STRUCTURES. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 2, pp. 5-26. DOI: https://doi.org/10.18500/0869-6632-2016-24-2-5-26
The research is devoted to a method of diagnostics and quantitative analysis of chaotic synchronization in the presence of noise. We analyze how the additive white normal noise influences the accuracy of the measurement of synchronization of chaos. We also propose a new modification of the standard algorithm, which significantly reduces the sensitivity of the method to the noise. Importance of the study is caused by its perspectives for fundamental researches of general properties of chaotic synchronization, as well as for practical applications to searching interconnections between oscillations in systems of different nature. This is especially important in biological and medical investigations where the level of noise is usually very large and the interference can not be removed. Thus, possibility of measuring of the level of interconnection between oscillations in different biological samples allows to detect hidden mechanisms existing between them. The researches are carried out by the method of numerical simulations. The model under study is a system of two uni-directionally coupled logistic maps, which is one of the most simple model in the nonlinear dynamics. From the other side, it allows to explore all general properties of coupled self-sustained oscillators with period-doubling bifurcations. The results of the researches have demonstrates that the basic correlative method of measurement of chaotic synchronization is valid only when the noise is absent or very small. The proposed in the work algorithm, which is based on using time lag between the estimated signals, can significantly improve the accuracy of measurements in the presence of noise. It can be applied to measurement of chaotic synchronization for a wide class of dynamical systems, in the cases when the statistical properties of chaotic attractors remain similar for both synchronous and non-synchronous regimes.
DOI:10.18500/0869-6632-2016-24-2-27-40
Paper reference: Shabunin A.V. Diagnostics and measurement of chaotic synchronization in the presence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24, Issue 2. P. 27-40.
1. Kuznetsov A.P., Kuznetsov S.P., Trubetskov D.I. Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. Part 1 // Izvestiya VUZ. Applied Nonlinear Dynamics. 2015. Vol. 23, No 5. P. 5–40 (in Russian).
2. Pierce J.R. Traveling-Wave Tubes // Bell System Technical Journal. 1950. Vol. 29, No 3. P. 390–460.
3. Weinstein L.A., Solntsev V.A. Lectures on Microwave Electronics. Moscow: «Sov. Radio», 1973. 400 p. (in Russian).
4. Shevchik V.N., Trubetskov D.I. Analytical Methods of Calculation in Microwave Electronics. Moscow: «Sov. Radio», 1970. 584 p. (in Russian).
5. Trubetskov D.I., Hramov A.E. Lectures on Microwave Electronics for Physicists. Vol. 1. Moskow: «Fizmatlit», 2003 (in Russian).
6. Gilmour A.S. Principles of Traveling Wave Tubes. Artech House, 1994. 625 p.
7. Trubetskov D.I., Titov A.V., and Funtov A.A. Interference amplification in an electron-wave tube (Linear theory) // Technical Physics Letters. 2013. Vol. 39, No 11. P. 977–981.
8. Godin O.A., Mokhov A.V. Amplification of sound in resonance interaction with fluid flow // Soviet physics. Acoustics. 1991. Vol. 37, No 1. P. 29–32.
9. Andronov A.A., Fabrikant A.L. Landau damping, wind waves and whistle // Nonlinear Waves. Moscow: «Nauka», 1979. P. 68–104 (in Russian).
10. Andronov A.A., Fabrikant A.L. Theory of the aerodynamic self-excitation of sound Amplification of surface waves // Soviet Physics. Acoustics. 1980. Vol. 26. P. 370–374.
11. Rabinovich M.I., Trubetskov D.I. Oscillations and Waves in Linear and Nonlinear Systems. Kluwer Academic Publisher, 1989. 578 p.
12. Lifshitz E.M., Pitaevskii L.P. Physical Kinetics. Course of Theoretical Physics. Vol. 10. Oxford: Pergamon Press, 1981. 452 p.
13. Kuznetsov S.P. Numerical simulation of noise amplification in broadband TWT // Lectures on UHF Electronics and Radio-physics. Saratov State University. 1981. Vol. 5. P. 165–176 (in Russian).
14. Gavrilov M.V., Trubetskov D.I. Effect of external high-frequency field on the behavior of the beam in the Caino gun: Linear theory accounting the virtual cathode // Lectures on UHF Electronics. Saratov State University, 1974. Vol. 5. P. 184–192 (in Russian).
15. Electronics of Backward-Wave Tubes / Eds V.N. Shevchik, D.I. Trubetskov. Saratov: Saratov University Publ., 1975. 195 p. (in Russian).
BibTeX
author = {A. P. Kuznetsov and Sergey P. Kuznetsov},
title = {ANALOGY IN INTERACTIONS OF ELECTRONIC BEAMS AND HYDRODYNAMIC FLOWS WITH FIELDS OF RESONATORS AND PERIODIC STRUCTURES},
year = {2016},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {24},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/analogy-in-interactions-of-electronic-beams-and-hydrodynamic-flows-with-fields-of-0},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2016-24-2-5-26},pages = {5--26},issn = {0869-6632},
keywords = {Chaotic oscillations,synchronization of chaos,measurement of synchronization},
abstract = {The research is devoted to a method of diagnostics and quantitative analysis of chaotic synchronization in the presence of noise. We analyze how the additive white normal noise influences the accuracy of the measurement of synchronization of chaos. We also propose a new modification of the standard algorithm, which significantly reduces the sensitivity of the method to the noise. Importance of the study is caused by its perspectives for fundamental researches of general properties of chaotic synchronization, as well as for practical applications to searching interconnections between oscillations in systems of different nature. This is especially important in biological and medical investigations where the level of noise is usually very large and the interference can not be removed. Thus, possibility of measuring of the level of interconnection between oscillations in different biological samples allows to detect hidden mechanisms existing between them. The researches are carried out by the method of numerical simulations. The model under study is a system of two uni-directionally coupled logistic maps, which is one of the most simple model in the nonlinear dynamics. From the other side, it allows to explore all general properties of coupled self-sustained oscillators with period-doubling bifurcations. The results of the researches have demonstrates that the basic correlative method of measurement of chaotic synchronization is valid only when the noise is absent or very small. The proposed in the work algorithm, which is based on using time lag between the estimated signals, can significantly improve the accuracy of measurements in the presence of noise. It can be applied to measurement of chaotic synchronization for a wide class of dynamical systems, in the cases when the statistical properties of chaotic attractors remain similar for both synchronous and non-synchronous regimes. DOI:10.18500/0869-6632-2016-24-2-27-40 Paper reference: Shabunin A.V. Diagnostics and measurement of chaotic synchronization in the presence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24, Issue 2. P. 27-40. Download full version }}