For citation:
Bezruchko B. P., Jalnine A. Y., Prokhorov M. D., Seleznev E. P. Large discrete nonlinear models of periodically driven RL-diode circuit. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 2, pp. 48-62.
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Russian
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530.18
Large discrete nonlinear models of periodically driven RL-diode circuit
Autors:
Bezruchko Boris Petrovich, Saratov State University
Jalnine Aleksej Yurevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Seleznev Evgeny Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract:
By experimental observables of natural and driven oscillations the point maps modeling complicated dynamics of periodically driven diode resonator are constructed and investigated. The place of the proposed maps among other mathematical models of this popular radiophysical system is discussed.
Key words:
Acknowledgments:
The work was supported by the Russian Foundation for Basic Research, grant N 96-02-16755, as well as with the support of INTAS, grant 93-2492-ext, within the framework of the program of the International Center for Fundamental Physics in Moscow.
Reference:
- Linsay PS. Period doubling and chaotic behavior in а driven anharmonic oscillator. Phys. Rev. Lett. 1981;47(19):1349-1352. DOI: 10.1103/PhysRevLett.47.1349.
- Kaplan AE, Kravtsov YuA, Rylov VA. Parametric Generators and Frequency Dividers. M.: Sovetskoe Radio; 1966. 333 p. (in Russian).
- Testa J, Perez J, Jeffries С. Evidence for universal behavior of a driven nonlinear oscillator. Phys. Rev. Lett. 1982;48(11):714-717. DOI: 10.1103/PhysRevLett.48.714.
- Hunt ЕR. Comment on a driven nonlinear oscillator. Phys. Rev. Lett. 1982;49(14):1054-1054. DOI: 10.1103/PhysRevLett.49.1054.
- Testa J, Perez J, Jeffries С. Testa, Perez and Jeffries respond. Phys. Rev. Lett. 1982;49(14):1055-1055. DOI: 10.1103/PhysRevLett.49.1055.
- Jeffries C, Perez J. Observation of а Pomeau—Manneville intermittent route to chaos in а nonlinear oscillator. Phys. Rev. А. 1982;26(4):2117-2122. DOI: 10.1103/PhysRevA.26.2117.
- Bezruchko BP, Kuznetsov SP, Seleznev ЕP, Yavorskaya EE. A transition to chaos in a nonlinear oscillator under impulse periodic influence. In: Lectures on Microwave Electronics and Radiophysics. Vol. 2. Saratov: Saratov University Publishing; 1984. P. 36.
- Kipchatov АA. Peculiarities of the complicated dynamics of a driven nonlinear oscillator. Radiophys. Quantum Electron. 1990;33(2):139-146. DOI: 10.1007/BF01040814.
- Baxter JH, Bocko MF, Douglass DH. Behavior of а nonlinear resonator driven at subharmonic frequencies. Phys Rev. А. 1990;41(2):619-625. DOI: 10.1103/physreva.41.619.
- Balberg I, Arbell H. Temperature as а bifurcation parameter in nonlinear electronic circuits. Phys. Rev. E. 1994;49(1):110-113. DOI: 10.1103/physreve.49.110.
- Linsay PS. Nonlinear dynamics in driven and autonomous electronic circuits. In: Carroll T, Pecora L, editors. Nonlinear Dynamics in Circuits. Singapore: World Scientific; 1995. P. 3-33. DOI: 10.1142/9789812830609_0001.
- Bronson SD, Dewey D, Linsay PS. Self-replicating attractor of а driven semiconductor oscillator. Phys. Rev. А. 1983;28(2):1201-1203. DOI: 10.1103/PhysRevA.28.1201.
- Klinker T, Meyer—Ilse W, Lauterborn W. Period doubling and chaotic behavior in а driven Toda oscillator. Phys. Lett. А. 1984;101(8):371-375. DOI: 10.1016/0375-9601(84)90604-2.
- Astakhov VV, Bezruchko VP, Seleznev EP. Study of the dynamics of a nonlinear oscillatory circuit under harmonic influence. Sov. J. Comm. Tech. Electron. 1987;32(12):2558-2566. (in Russian).
- Buskirk R, Jeffries С. Observation of chaotic dynamics of coupled nonlinear oscillators. Phys. Rev. A. 1985;31(5):3332-3357. DOI: 10.1103/PhysRevA.31.3332.
- Rollins RW, Hunt ER. Exactly solvable model of a physical system exhibiting universal chaotic behavior. Phys. Rev. Lett. 1982;49(18):1295-1298. DOI: 10.1103/PhysRevLett.49.1295.
- Perez J. Mechanism for global features of chaos in а driven nonlinear oscillator. Phys. Rev. А. 1985;32(4):2513-2516. DOI: 10.1103/physreva.32.2513.
- Yoon TH, Song JW, Shin SY, Rа JW. One—dimensional map and its modification for periodic—chaotic sequence in а driven nonlinear oscillator. Phys. Rev. А. 1984;30(6):3347-3350. DOI: 10.1103/PhysRevA.30.3347.
- Matsumoto T, Chua LO, Tanaka S. Simplest chaotic nonautonomous circuit. Phys. Rev. А. 1984;30:1155-1157. DOI: 10.1103/PhysRevA.30.1155.
- Hunt ER, Rollins RW. Exactly solvable model of a physical system exhibiting multi—dimensional chaotic behavior. Phys. Rev. А. 1984;29(2):1000-1002. DOI: 10.1103/PhysRevA.29.1000.
- Su Z, Rollins RW, Hunt ER. Simulation and characterization of strange attrators in driven diode resonator systems. Phys. Rev. А. 1989;40(5):2698-2705. DOI: 10.1103/PhysRevA.40.2698.
- Farmer JD, Sidorowich J. Predicting chaotic time series. Phys. Rev. Lett. 1987;59(8):845-848. DOI: 10.1103/PhysRevLett.59.845.
- Casdagli M. Nonlinear prediction of chaotic time series. Physica D. 1989;35(3):335-356. DOI: 10.1016/0167-2789(89)90074-2.
- Breeden JL, Hubler A. Reconstructing equations of motion from experimental data with unobserved variables. Phys. Rev. A. 1990;42(10):5817-5826. DOI: 10.1103/physreva.42.5817.
- Gribkov DA, Gribkova VV, Kravtsov YuA, Kuznetsov YuI, Rzhanov AG. Restoring the structure of the dynamic system by time series. J. Comm. Tech. Electron. 1994;39(2):269-277.
- Abarbanel HDI, Brown R, Kadtke JB. Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra. Phys. Rev. A. 1990;41(4):1782-1807. DOI: 10.1103/physreva.41.1782.
- Brown R, Rulkov NF, Tracy ER. Modeling and synchronizing chaotic systems from time—series data. Phys. Rev. Е. 1994;49(5):3784-3800. DOI: 10.1103/physreve.49.3784.
- Yanson NB, Anishchenko VS. Modeling the dynamical systems based on experimental data. Izvestiya VUZ. Applied Nonlinear Dynamics. 1995;3(3):112-121. (in Russian).
- Gencay R, Dechert WD. An algorithm for the n Lyapunov exponents of an n—dimensional unknown dynamical system. Physica D. 1992;59(1-3):142-157. DOI: 10.1016/0167-2789(92)90210-E.
Received:
05.03.1997
Accepted:
22.04.1997
Published:
17.07.1997
Journal issue:
- 36 reads