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

For citation:

Izmailov I. V., Ljachin A. V., Poizner B. N., Shergin D. A. Spatial deterministic chaos: the model and demonstration of phenomenon in computing experiment. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 1, pp. 123-136. DOI: 10.18500/0869-6632-2005-13-1-123-136

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2005no1-2p123_0.pdf
(downloads: 144)
Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
535:530.182 + 519.713
DOI: 
10.18500/0869-6632-2005-13-1-123-136

Spatial deterministic chaos: the model and demonstration of phenomenon in computing experiment

Autors: 
Izmailov Igor Valerevich, National Research Tomsk State University
Ljachin Aleksandr Vladimirovich, National Research Tomsk State University
Poizner Boris Nikolaevich, National Research Tomsk State University
Shergin Denis Aleksandrovich, National Research Tomsk State University
Abstract: 

The concept of spatial deterministic chaos is justified. An attempt to give its settheoretic definition is undertaken. Transition from the ordinary differential equations to discrete maps without use of an approximation of the instantaneous response is realized for mathematical description of spatial deterministic chaos. The developed theoretical theses are applied for deriving a dynamics model in terms of discrete maps of nonlinear phase shift in a ring interferometer. In case of the model discrete realizations, phase portraits Fourier’s spectrums illustrating peculiarities of spatial deterministic chaos in the ring interferometer are constructed. A concept of discrete maps undergoing an evolution is introduced. 

Key words: 
-
Reference: 
  1. Ikeda K. Multiple-valued stationary state and its instability of the transmitted light by ring cavity system. Opt. Commun. 1979;30(2):257–261. DOI: 10.1016/0030-4018(79)90090-7.
  2. Akhmanov SA, Vorontsov MA. Instabilities and structures in coherent nonlinear optical systems covered by two-dimensional feedback. In: Nonlinear Waves: Dynamics and Evolution: Collection of Articles. Moscow: Nauka; 1989. P. 228–237 (in Russian).
  3. Rozanov NN. Optical Bistability and Hysteresis in Distributed Nonlinear Systems. Moscow: Nauka; 1997. 336 p. (in Russian).
  4. Izmailov IV, Kalayda VT, Magazinnikov AL, Poizner BN. Bifurcations in a point model of a ring interferometer with delay and field rotation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(5):47–59 (in Russian).
  5. Kuznetsov SP. Dynamic Chaos. Lecture Course. Textbook for University Students Enrolled in Physical Specialties. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  6. Balyakin AA. Investigation of the chaotic dynamics of a ring nonlinear resonator under a two-frequency external action. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(4–5):3–15 (in Russian).
  7. Berge P, Pomeau I, Vidal K. Order Within Chaos. Wiley; 1987. 329 p.
  8. Melnikov LA, Konyukhov AI, Ryabinina MV. Dynamics of the transverse polarization structure of the field in lasers. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(6):33–53 (in Russian).
  9. Weiss CO et al. Solitons and vortices in lasers. Appl. Phys. B. 1999;68(2):151–168. DOI: 10.1007/s003400050601.
  10. Izmailov IV, Poizner BN. Implementation options for a nonlinear optical device for covert information transmission. Atmospheric and Oceanic Optics. 2001;14(11):1074–1086 (in Russian).
  11. Melnikov LA, Konukhov AI, Veshneva IV et al. Nonlinear dynamics of spatial and temporal patterns in lasers and atom optics: Kerr-lens mode-locked laser, Zeeman laser and Bose-Einstein atomic condensate. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(3):40–62 (in Russian).
  12. Ryskin MI, Ivanov AV. Nonlinear dynamics in earth sciences. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(6):138–148 (in Russian).
  13. Izmailov IV, Poizner BN, Denisov PE. Equivalence: From substantiating a concept to analyzing bifurcation behavior. In: Bulletin of the TSU. Bulletin of Operational Scientific Information. No. 15. Tomsk: TSU; 2003. 46 p. (in Russian).
  14. Zaslavsky GM, Kirichenko NA. Dynamic chaos. In: Prokhorov AM, editor. Physical Encyclopedia. Vol. 5. Moscow: Sov. Encyclopedia; 1998. P. 397–402 (in Russian).
  15. Arshinov AI, Mudarisov RR, Poizner BN. Formation mechanisms of the simplest optical structures in a nonlinear Fizeau interferometer. Russian Physics Journal. 1995;38(6):77–81 (in Russian).
  16. Izmailov IV, Magazinnikov AL, Poizner BN. Modeling processes in a ring interferometer with nonlinearity, delay and diffusion under nonmonochromatic radiation. Russian Physics Journal. 2000;43(2):29–35 (in Russian).
  17. Shergin DA, Izmailov IV. Discrete mappings as a means of describing deterministic spatial chaos. In: Collection of Abstracts of the 9th All-Russian Scientific Conference of Physics Students and Young Scientists: In 2 Volumes. Vol. 2. Ekaterinburg-Krasnoyarsk: Russian ERT; 2003. P. 90–93 (in Russian).
  18. Shergin DA, Izmailov IV, Poizner BN. Discrete mappings as a language for describing spatial deterministic chaos. In: Modern Problems of Physics and High Technologies: Proceedings of the International Conference. September 29 - October 4, 2003, Tomsk. Tomsk: STL Publishing; 2003. P. 186–189 (in Russian).
Received: 
30.08.2004
Accepted: 
29.03.2005
Published: 
30.09.2005
Short text (in English):
PDF icon a2005no1-2p123_0.pdf
(downloads: 99)
  • 1810 reads