ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Magazinnikov A. L., Poizner B. N., Sabdenov K. O., Timokhin A. M. Three Kerr media in nonlinear Fizeau interferometer: factors effecting on bifurcation behaviour. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 5, pp. 56-65. DOI: 10.18500/0869-6632-1998-6-5-56-65

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
535:530.162 + 519.713
DOI: 
10.18500/0869-6632-1998-6-5-56-65

Three Kerr media in nonlinear Fizeau interferometer: factors effecting on bifurcation behaviour

Autors: 
Magazinnikov Anton Leonidovich, National Research Tomsk State University
Poizner Boris Nikolaevich, National Research Tomsk State University
Sabdenov Kanysh Orakbaevich, National Research Tomsk State University
Timokhin Anatoly Mikhailovich, National Research Tomsk State University
Abstract: 

Optical formation processes in Fizeau interferometer containing three nonlinear media are defined by three ordinary differential equations involving nonlinearities of the function cos—form. Stability analysis of equations stationary decisions under strong nonlinearities disclosed the presence of many stationary stable and unstablc states. Liapunov’s exponents found by numerical methods proved that different motion types (including dynamical chaos) exist in the optical system. Possibility of the Fizean interferometer nonlinear dynamics control by means of three initial conditions and nonlinear parameters choice is shown.

Key words: 
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Acknowledgments: 
This work was supported in part by the ISSEP Foundation (grant № d98-253).
Reference: 
  1. Akhmanov SA, Vorontsov MA, editors. New Physical Principles of Optical Information Processing. М.: Nauka; 1990. 398 p. (in Russian).
  2. Balanov AG, Vadivasova TE, Postnov DE, Sosnovtseva OV. Bifurcation of chaos synchronization in the Ressler oscillator with harmonic influence. Izvestiya VUZ. Applied Nonlinear Dinamics. 1997;5(5):31-43. (in Russian).
  3. Vorontsov MA, Razgulin АV. Properties of the global attractor of a nonlinear optical system with nonlocal couplings. Radioengineering. 1995;3:67-76. (in Russian).
  4. Kashchenko SA, Majorov VV, Myshkin IYu. Wave formations in ring neural systems. Math. Models Comp. Simulations. 1997;9(3):29-39. (in Russian).
  5. Larichev АV, Nikolaev IР, Chulichkov AL. Spatiotemporal period doubling in a nonlinear interferometer with distributed optical feedback. Opt. Lett. 1996;21(15):1180-1182. DOI: 10.1364/ol.21.001180.
  6. Arshinov AI, Mudarisov RR, Poizner BN. Three Kerr media in the ring interferometer: the role of non-identity. Izvestiya VUZ. Applied Nonlinear Dinamics. 1995;3(1):20-27. (in Russian).
  7. Arshinov AI, Lysenko AN, Mudarisov RR, Poizner BN. Transverse dynamics of the laser beam in a nonlinear optical system with two-dimensional feedback: interpretation of the results of a computational experiment. Izvestiya VUZ. Applied Nonlinear Dinamics. 1995;3(6):46-51. (in Russian).
  8. Lichtenberg АJ, Lieberman MA. Regular and Stochastic Motion. N.Y.: Springer; 1983. 499 p. DOI: 10.1007/978-1-4757-4257-2.
  9. Neimark YuI, Landa PS. Stochastic and Chaotic Oscillations. Berlin: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  10. Loskutov AYu, Mikhailov АS. Introduction to Synergetics. М.: Nauka; 1990. 269 p. (in Russian).
  11. Moon FC. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. New York: Wiley; 1987. 309 p.
  12. Kurdyumov SP, Malinetskii GG, Potapov AB. Non-stationary structures, dynamic chaos, cellular automata. In: New in Synergy. Mysteries of the World of Non-equilibrium Structures. М.: Nauka; 1996. P. 95-164. (in Russian).
Received: 
23.06.1998
Accepted: 
19.10.1998
Published: 
25.02.1999
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