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

For citation:

Astahov S. V., Vadivasova T. E., Anishchenko V. S. Studying of spatial transition to temporal chaos in active medium with unidirectional coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 2, pp. 122-130. DOI: 10.18500/0869-6632-2008-16-2-122-130

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 53)
Article type: 

Studying of spatial transition to temporal chaos in active medium with unidirectional coupling

Astahov Sergej Vladimirovich, Saratov State University
Vadivasova Tatjana Evgenevna, Saratov State University
Anishchenko Vadim Semenovich, Saratov State University

In the work a new model of a continuous active medium with unidirectional coupling of active elements is proposed. The Anishchenko–Astakhov oscillator was selected as an active element. The model shows both regular and chaotic in time regimes. The results obtained for the medium are compared with the results for a chain of Anishchenko– Astakhov oscillators. The problem of conformity between the discrete model and the continuous medium is analyzed.

Key words: 
  1. Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin: Springer-Verlag, 1984.
  2. Gaponov-Grekhov A.V., Rabinovich M.I. Dynamical chaos in ensembles of structures and spatial development of turbulence in unbounded systems / Ed. W. Ebeling. New York: Springer, 1986.
  3. Kaneko K. Spatiotemporal chaos in one- and two- dimensional coupled map lattices // Physica D. 1989. Vol. 32. P. 60.
  4. Лоскутов А.Ю., Михайлов А.С. Введение в синергетику. Москва: Наука, 1990.
  5. Кузнецов А.П., Кузнецов С.П. Критическая динамика решеток связанных отображений у порога хаоса // Изв. вузов. Радиофизика. 1991. Т. 34, No 10–12. С. 1079.
  6. Ланда П.С. Нелинейные колебания и волны. Москва: Наука, 1997.
  7. Bohr T., Jensen M.H., Paladin G., Vulpiani A. Dynamical systems approach to turbulence. New York: Cambridge University, 1998.
  8. Aranson I.S., Kramer L. The world of the complex Ginzburg–Landau equation // Rev. Mod. Phys. 2002. Vol. 74. P. 99.
  9. Anishchenko V.S. Auto-oscillatory regimes in the chain of coupled generators // Self-organization by Nonlinear Irreversible Processes. Proceedings of the Third International Conference, Kuhlungsborn, GDR, March 18–22, 1985. Berlin: Springer- Verlag, 1986. P. 198.
  10. Анищенко В.С., Арансон И.С., Постнов Д.Э., Рабинович М.И. Пространственная синхронизация и бифуркации развития хаоса в цепочке связанных генераторов // ДАН СССР. 1986. Т. 28, No 5. С. 1120.
  11. Kaneko K. Collapse of Tori and Genesis of Chaos in Dissipative Systems. Singapore:  World Scientific, 1986.
  12. Pikovsky A.S. Discrete model of spatially mixing system // Physics Letters A. 1992. Vol. 168. P. 276.
  13. Rudzick O., Pikovsky A. Unidirectionally coupled map lattice as a model for open flow systems// Physical Review E. 1996. Vol. 54, No 5. P. 5107.
Short text (in English):
(downloads: 43)