ADVANCED COMPUTING TOPOLOGICAL AND DYNAMICAL INVARIANTS OF RELATIVISTIC BACKWARD-WAVE TUBE TIME SERIES IN CHAOTIC AND HYPERCHAOTIC REGIMES

Автор(и)

  • A. Tsudik
  • A. Glushkov
  • V. Ternovsky
  • P. Zaichko

DOI:

https://doi.org/10.18524/0235-2435.2020.29.225596

Ключові слова:

relativistic backward-wave tube, , chaotic dynamics, non-linear methods

Анотація

Представлені уточнені дані обчислення динамічних і топологічних інваріантів (значення кореляційної розмірності, розмірності вкладення, Каплана-Йорка, показники Ляпунова, ентропія Колмогорова та ін) для часових рядів, що характеризують динаміку релятивістської лампи зверненої хвилі з урахуванням ефектів дисипації, просторового заряду і ін. в хаотичному і гіперхаотичному режимах. Отримані рішення системи рівнянь для одновимірної релятивістської фази електрона і одновимірної комплексної амплітуди поля. Отримані дані уточнюють раніше представлені дані для динамічних і топологічних інваріантів динаміки релятивістської лампи зворотної хвилі в хаотичному режимі і дозволяють кількісно охарактеризувати сценарій переходу до хаосу у часовій динаміці.

Посилання

Glushkov, A.V.; Prepelitsa, G.P.; Svinarenko, A.A. ; Zaichko, P.A. Studying interaction dynamics of the non-linear vibrational systems within non-linear prediction method (application to quantum autogenerators) In Dynamical Systems Theory; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T1, pp 467-477.

Ignatenko, A.V.; Buyadzhi, A.; Buyadzhi, V.; Kuznetsova,A.; Mashkantsev, A.; Ternovsky, E. Nonlinear chaotic dynamics of quantum systems: molecules in an electromagnetic field// Adv. Quant. Chem. 2018,78 doi.org/10.1016/bs.aiq.2018.06.006.

Ginsburg, H. S.; Kuznetsov, S.P.; Fedoseyev, T.N. Theory of transients in relativistic BWO. Izv. Vuzov. Ser. Radiophys. 1978, 21, 1037-1052.

Ginzburg, N.S.; Zaitsev, N.A.; Ilyakov, E.; Kulagin, V.I.; Novozhilov, Yu. Rosenthal P., Sergeev V., Chaotic generation in backward wave tube of the megawatt power level. Journ. of Techn.Phys. 2001, 71, 73-80.

Kuznetsov A.P., Kuznetsov S.P., Ryskin N.M., Isaeva O.B., Non-linearity: From oscillations to chaos.-Moscow: NIS RHD.-2006.

Kuznetsov A.P., Shirokov A.P., Discretre model of relativistic backward-wave tube. Russian J.of Phys. Ser.PND. 1997. 5, 76-83.

Kuznetsov S.P., Trubetskov D.I., Chaos and hyperchaos in backward-wave tube. Russian Journ.of Phys. Ser.Radiophys.-2004, XLVII(5), 1-8

Ryskin N.M., Titov V.N., The transition to the development of chaos in a chain of two unidirectionally-coupled backward-wave tubes. Journ.Techn.Phys. 2003. 73, 90-94.

Glushkov, A.V.; Buyadzhi, V.V.; Ternovsky V.B. Geometry of Chaos: Consistent combined approach to treating of chaotic self-oscillations in backward-wave tube. Proc. Intern. Geometry Center. 2013, 6(2), 6-12.

Ternovsky V.B., Geometry and Dynamics of a Chaos: Modelling non-linear processes in relativistic backward-wave tubes chain. Proc. of Int. Geom. Center. 2014, 7(3), 79-86

A.V. Glushkov, A.V. Tsudik, D.A. Novak, O.B. Dubrovsky, Chaotic dynamics of relativistic backward-wave tube with accounting for space charge field and dissipation effects: New effects. Photoelectronics. 2018. 27, 44-51.

Levush, В.; Antonsen, T.M.; Bromborsky, A.; Lou, W.R.; Carmel, Y. Theory of relativistic backward wave oscillator with end reflections. IEEE Trans. on Plasma Sci. 1992, 20, 263-280.

Ryskin, N.M.; Titov, V.N. Self-modulation and chaotic regimes of generation in a relativistic backward-wave oscillator with end reflections. Radiophys. and Quant.Electr. 2001, 44, 793-806.

Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A.; Prepelitsa, G.P. Energy approach to atoms in a laser field and quantum dynamics with laser pulses of different shape. In Coherence and Ultrashort Pulsed Laser Emission. Duarte, F.J., Ed.; InTech: Rijeka, 2010, 159-186.

Levush, В.; Antonsen, Т.; Bromborsky, А.; Lou, W. Relativistic backward wave oscillator: theory and experiment. Phys.Fluid. 1992, B4, 2293-2299.

Glushkov, A.V. Methods of a Chaos Theory. OSENU: Odessa, 2012.

Glushkov, A.V. Atom in an electromagnetic field. KNT: Kiev, 2005.

Glushkov, A.V.; Khetselius, O.Yu.; Brusentseva, S.V.; Zaichko, P.A.; Ternovsky, V.B. Studying interaction dynamics of chaotic systems within a non-linear prediction method: Application to neurophysiology In Advances in Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Advances in Computer Engineering; Balicki, J., Ed.; WSEAS Press: Gdansk, 2014; Vol 21, pp 69-75.

Khetselius, O.Yu. Forecasting evolutionary dynamics of chaotic systems using advanced non-linear prediction method In Dynamical Systems Applications; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T2, pp 145-152..

Glushkov, A.V.; Malinovskaya, S.V.; Gurnitskaya, E.P.; Khetselius, O.Yu.; Dubrovskaya, Yu.V. Consistent quantum theory of recoil induced excitation and ionization in atoms during capture of neutron. J. Phys.: Conf. Ser. 2006, 35, 425-430.

Khetselius, O.Yu. Hyperfine structure of atomic spectra. Astroprint: Odessa, 2008.

Khetselius, O.Yu. Quantum structure of electroweak interaction in heavy finite Fermi-systems. Astroprint: Odessa, 2011.

Glushkov, A.V. Relativistic Quantum theory. Quantum mechanics of atomic systems. Astroprint: Odessa, 2008.

Glushkov, A.V., Khetselius, O.Yu., Svinarenko, A.A., Buyadzhi, V.V. Spectroscopy of autoionization states of heavy atoms and multiply charged ions. TEC: Odessa, 2015

Glushkov, A.V. Relativistic and correlation effects in spectra of atomic systems. Astroprint: Odessa, 2006.

Glushkov, A.V.; Prepelitsa, G.P.; Svinarenko, A.A. ; Zaichko, P.A. Studying interaction dynamics of the non-linear vibrational systems within non-linear prediction method (application to quantum autogenerators) In Dynamical Systems Theory; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T1, pp 467-477.

Abarbanel, H.; Brown, R.; Sidorowich, J; Tsimring, L. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 1993, 65, 1331- 1392.

Packard, N.; Crutchfield, J; Farmer, J.; Shaw, R. Geometry from a time series Phys. Rev. Lett. 1988, 45, 712-716.

Kennel, M.; Brown, R.; Abarbanel, H. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A. 1992, 45, 3403-3412.

Packard N., Crutchfield J., Farmer J., Shaw R., Geometry from a time series//Phys Rev Lett.-1988.-Vol.45.-P.712–716.

Gallager, R. Information theory and reliable communication. N.-Y., 1986.

Grassberger, P. ; Procaccia, I. Measuring the strangeness of strange attractors. Physica D. 1983, 9, 189-208.

Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J. Testing for nonlinearity in time series: The method of surrogate data. Physica D. 1992, 58, 77-94.

Glushkov, A.V.; Malinovskaya, S.V.; Loboda, A.V.; Shpinareva, I.M.; Gurnitskaya, E.P.; Korchevsky, D.A. Diagnostics of the collisionally pumped plasma and search of the optimal plasma parameters of x-ray lasing: calculation of electron-collision strengths and rate coefficients for Ne-like plasma. J. Phys.: Conf. Ser. 2005, 11, 188-198.

Taken, F. Detecting strange attractors in turbulence. Lecture notes in mathematics (Springer) 1981, 898, 366–381.

Glushkov, A.V.; Buyadzhi, V.V.; Ponomarenko, E.L. Geometry of Chaos: Advanced approach to treating chaotic dynamics in some nature systems// Proc. Intern. Geom. Center. 2014 7(1),24-30.

Sano, M.; Y. Sawada, Y. Measurement of the Lyapunov spectrum from chaotic time series. Phys Rev.Lett. 1995, 55, 1082-1085

Rusov V., Glushkov A., Vaschenko V., Korchevsky D., Ignatenko A. Stochastic dynamics of the atomic systems in the crossed electric and magnetic field: the rubidium atom recurrence spectra. Bull.of Kiev Nat. Univ. 2004, N4, 433.

Khetselius, O. Relativistic perturbation theory calculation of the hyperfine structure parameters for some heavy-element isotopes. Int. J. Quant.Chem. 2009, 109, 3330-3335.

Khetselius, O. Relativistic calculation of the hyperfine structure parameters for heavy elements and laser detection of the heavy isotopes. Phys.Scr. 2009, T135, 014023.

Glushkov, A.; Gurskaya, M.; Ignatenko, A.; Smirnov, A.; Serga, I.; Svinarenko, A.; Ternovsky E. Computational code in atomic and nuclear quantum optics: Ad-vanced computing multiphoton resonance parameters for atoms in a strong laser field. J. Phys.: Conf. Ser. 2017, 905, 012004.

Buyadzhi, V., Zaichko, P., Antoshkina, O., Kulakli, T., Prepelitsa, P., Ternovsky, V., Mansarliysky, V. Computing of radiation parameters for atoms and multicharged ions within relativistic energy approach: Advanced Code. J. Phys.: Conf. Ser. 2017, 905(1), 012003.

Svinarenko, A., Glushkov, A., Khetselius, O., Ternovsky,V., Dubrovskaya, Yu., Kuznetsova, A., Buyadzhi, V. Theoretical spectroscopy of rare-earth elements: spectra and autoionization resonances. Rare Earth Element, InTech. 2017, 83-104.

Glushkov A.V., Khetselius O.Yu., Loboda A.V., Ignatenko A., Svinarenko A., Korchevsky D., Lovett L., QED Approach to Modeling Spectra of the Multicharged Ions in a Plasma: Oscillator and Electron‐ion Collision Strengths. AIP Conference Proceedings.-2008. 1058, 175-177

Glushkov, A., Khetselius, O., Svinarenko A.A., Buyadzhi, V.V., Ternovsky, V., Kuznetsova, A., Bashkarev, P. Relativistic perturbation theory formalism to computing spectra and radiation characteristics: application to heavy element. Recent Studies in Perturbation Theory. InTech. 2017, 131-150.

Glushkov, A.V.; Malinovskaya, S.V.; Prepelitsa, G.P.; Ignatenko, V. Manifestation of the new laser-electron nuclear spectral effects in the thermalized plasma: QED theory of co-operative laser-electron-nuclear proces-ses. J. Phys.: Conf. Ser. 2005, 11, 199-206.

Ivanova, E.P., Ivanov, L.N., Glushkov, A., Kramida, A. High order corrections in the relativistic perturbation theory with the model zeroth approximation, Mg-Like and Ne-Like Ions. Phys. Scripta 1985, 32, 513-522.

Prepelitsa, G.; Glushkov, A.V.; Lepikh, Ya.; Buyadzhi, V.; Ternovsky, V.; Zaichko, P. Chaotic dynamics of non-linear processes in atomic and molecular systems in electromagnetic field and semiconductor and fiber laser devices: new approaches, uniformity and charm of chaos. Sensor Electr. and Microsyst.Techn. 2014, 11, 43-57.

##submission.downloads##

Опубліковано

2021-02-26

Номер

Розділ

Статті