Надіслати цю статтю Про оцінку старшого показника Ляпунова моделі хрестоподібних хвиль у прямокутному каналі скінченних розмірів
Анотація
Зразок для цитування: В. Д. Печук, Т. С. Краснопольська, “Про оцінку старшого показника Ляпунова моделі хрестоподібних хвиль у прямокутному каналі скінченних розмірів,” Мат. методи та фіз.-мех. поля, 65, No. 1-2, 209–215 (2022), https://doi.org/10.15407/mmpmf2022.65.1-2.209-215
Translation: V. D. Pechuk, T. S. Krasnopolska, “Estimation of the largest Lyapunov exponent for a model of cross-shaped waves in a rectangular channel of finite size,” J. Math. Sci., 282, No. 5, 862–869 (2024), https://doi.org/10.1007/s10958-024-07221-xКлючові слова
Посилання
P. Bergé, Y. Pomeau, C. Vidal, Order Within Chaos: Towards a Deterministic Approach to Turbulence, J. Wiley & Sons, New York (1984).
V. A. Golovko, “Neural network methods for processing chaotic processes,” in: Yu. V. Tyumentsev (ed.), Lectures on Neuroinformatics, Proc. of Scientific Session MEPhI-2005, VII All-Russian Scientific and Technical Conference “Neuroinformatics-2005”, MEPhI, Moscow (2005), pp. 43–91 (in Russian).
T. S. Krasnopol’skaya, A. Y. Shvets, “Properties of chaotic fluid oscillations in cylindrical basins,” Prikl. Mekh., 28, No. 6, 52–61 (1992) (in Russian); English translation: Int. Appl. Mech., 28, No. 6, 386–394 (1992), https://doi.org/10.1007/BF00847097
T. S. Krasnopol’skaya, A. Y. Shvets, “Chaotic oscillations of a spherical pendulum as an example of interaction with an energy source,” Prikl. Mekh., 28, No. 10, 61–68 (1992) (in Russian); English translation: Int. Appl. Mech., 28, No. 10, 669–674 (1992), https://doi.org/10.1007/BF00846923
S. P. Kuznetsov, Dynamic Chaos [in Russian], Fizmatlit. Moscow (2001).
F. C. Moon, Chaotic Vibrations: An Introduction for Applied Scientists and Engineers, J. Wiley & Sons, New York (1987).
V. I. Oseledets, “A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems,” Tr. Mosk. Mat. Obshch., 19, 179–210 (1968) (in Russian); English translation: Trans. Moscow Math. Soc., 19, 197–231 (1968).
A. Y. Shvets, V. A. Sirenko, “Scenarios of transitions to hyperchaos in nonideal oscillating systems,” Nelin. Kolyv., 21, No. 2, 284–292 (2018) (in Russian); English translation: J. Math. Sci., 243, No. 2, 338–346 (2019), https://doi.org/10.1007/s10958-019-04543-z
G. Benettin, L. Galgani, A. Giorgilli, J.-M. Strelcyn, “Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory,” Meccanica, 15, No. 1, 9–20 (1980), https://doi.org/10.1007/BF02128236
G. Benettin, L. Galgani, J. M. Strelcyn, “Kolmogorov entropy and numerical experiments,” Phys. Rev. A, 14, No. 6, 2338–2342 (1976), https://doi.org/10.1103/PhysRevA.14.2338
J. P. Crutchfield, J. D. Farmer, N. H. Packard, R. S. Shaw, “Chaos,” Sci. Am., 255, No. 6, 46–57 (1986), http://doi.org/10.1038/scientificamerican1286-46
T. S. Krasnopolskaya, “Acoustic chaos caused by the Sommerfeld effect,” J. Fluid Struct., 8, No. 7, 803–815 (1994), https://doi.org/10.1016/S0889-9746(94)90300-X
T. S. Krasnopolskaya, “Chaos in acoustic subspace raised by the Sommerfeld –Kononenko effect,” Meccanica, 41, No. 3, 299–310 (2006), https://doi.org/10.1007/s11012-005-5899-z
T. S. Krasnopolskaya, G. J. F. Heijst, “Wave pattern formation in a fluid annulus with a radially vibrating inner cylinder,” J. Fluid Mech., 328, 229–252 (1996), https://doi.org/10.1017/S0022112096008701
T. S. Krasnopolskaya, V. V. Meleshko, G. W. M. Peters, H. E. H. Meijer, “Mixing in Stokes flow in an annular wedge cavity,” Eur. J. Mech. B-Fluids, 18, No. 5, 793–822 (1999), https://doi.org/10.1016/S0997-7546(99)00119-3
T. S. Krasnopolskaya, E. D. Pechuk, “Peculiarities of parametric resonances in cross-waves,” Chaotic Modeling and Simulations, No. 3, 377–385 (2016).
J. Laskar, C. Froeschlé, A. Celletti, “The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping,” Physica D: Nonlinear Phenomena, 56, Nos. 2-3, 253–269 (1992), https://doi.org/10.1016/0167-2789(92)90028-L
V. Meleshko, T. Krasnopolskaya, G. W. M. Peters, H. E. H. Meijer, “Coherent structures and scales of Lagrangian turbulence,” in: S. Gavrilakis, L. Machiels, P. A. Monkewitz (eds), Advances in Turbulence VI, Vol. 36 of Ser. Fluid Mechanics and its Applications, Springer, Dordrecht (1996), pp. 601–604, https://doi.org/10.1007/978-94-009-0297-8_171
A. Y. Shvets, T. S. Krasnopolskaya, “Hyperchaos in piezoceramic systems with limited power supply,” in: A. V. Borisov, V. V. Kozlov, I. S. Mamaev, M. A. Sokolovskiy (eds), Proc. of IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Vol. 6 of IUTAM Bookseries, Springer, Dordrecht (2008), pp. 313–322, https://doi.org/10.1007/978-1-4020-6744-0_27
A. Shvets, S. Donetskyi, “Transition to deterministic chaos in some electroelastic systems,” in: C. H. Skiadas, I. Lubashevsky (eds), Proc. of 11th Chaotic Modeling and Simulation International Conference CHAOS 2018, Springer Proceedings in Complexity, Springer, Cham (2019), pp. 257–264, https://doi.org/10.1007/978-3-030-15297-0_23
F. Takens, “Detecting strange attractors in turbulence,” in: D. Rand, L. S. Young (eds), Dynamical Systems and Turbulence, Vol. 898 of Lecture Notes in Mathematics, Springer, Berlin–Heidelberg (1981), pp. 366–381, https://doi.org/10.1007/BFb0091924
A. Wolf, J. B. Swift, H. L. Swinney, J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D: Nonlinear Phenomena, 16, No. 3, 285–317 (1985), https://doi.org/10.1016/0167-2789(85)90011-9
Посилання
- Поки немає зовнішніх посилань.
Ця робота ліцензована Creative Commons Attribution 3.0 License.