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 PDF(Ru):
PDF icon 2008no2p122.pdf
(downloads: 118)
Language: 
Russian
Heading: 
Journal in the journal
Article type: 
Article
UDC: 
530.182::52.072.127
DOI: 
10.18500/0869-6632-2008-16-2-122-130

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

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

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: 
-
Reference: 
  1. Kuramoto Y. Chemical Oscillations, Waves, and Turbulence. Berlin: Springer-Verlag; 1984. 158 p. DOI: 10.1007/978-3-642-69689-3.
  2. Gaponov-Grekhov AV, Rabinovich MI. Dynamical chaos in ensembles of structures and spatial development of turbulence in unbounded systems. In: Ebeling W, Ulbricht H, editors. Selforganization by Nonlinear Irreversible Processes. Berlin: Springer; 1986. P. 37–46. DOI: 10.1007/978-3-642-71004-9_4.
  3. Kaneko K. Spatiotemporal chaos in one- and two- dimensional coupled map lattices. Physica D. 1989;37(1–3):60–82. DOI: 10.1016/0167-2789(89)90117-6.
  4. Loskutov AY, Mikhailov AS. Introduction to Synergetics. Moscow: Nauka; 1990. 272 p. (in Russian).
  5. Kuznetsov AP, Kuznetsov SP. Critical dynamics of coupled-map lattices at onset of chaos (review). Radiophys. Quantum Electron. 1991;34(10–12):845–868. DOI: 10.1007/BF01083617.
  6. Landa PS. Nonlinear Oscillations and Waves in Dynamical Systems. Dordrecht: Springer; 1996. 544 p. DOI: 10.1007/978-94-015-8763-1.
  7. Bohr T, Jensen MH, Paladin G, Vulpiani A. Dynamical Systems Approach to Turbulence. New York: Cambridge University; 1998. 350 p. DOI: 10.1017/CBO9780511599972.
  8. Aranson IS, Kramer L. The world of the complex Ginzburg–Landau equation. Rev. Mod. Phys. 2002;74(1):99–143. DOI: 10.1103/RevModPhys.74.99.
  9. Anishchenko VS. Auto-oscillatory regimes in the chain of coupled generators. In: Ebeling W, Ulbricht H, editors. Selforganization by Nonlinear Irreversible Processes. Berlin: Springer; 1986. P. 198–202. DOI: 10.1007/978-3-642-71004-9_26.
  10. Anishchenko VS, Aranson IS, Postnov DE, Rabinovich MI. Spatial synchronization and bifurcations of the development of chaos in a chain of coupled generators. Proc. Acad. Sci. USSR. 1986;28(5):1120–1124 (in Russian).
  11. Kaneko K. Collapse of Tori and Genesis of Chaos in Dissipative Systems. World Scientific, Singapore; 1986. 276 p. DOI: 10.1142/0175.
  12. Pikovsky AS. Discrete model of spatially mixing system. Phys. Lett. A. 1992;168(4):276–279. DOI: 10.1016/0375-9601(92)91131-A.
  13. Rudzick O, Pikovsky A. Unidirectionally coupled map lattice as a model for open flow systems. Phys. Rev. E. 1996;54(5):5107–5115. DOI: 10.1103/PhysRevE.54.5107.
Received: 
04.12.2007
Accepted: 
25.02.2008
Published: 
30.04.2008
Short text (in English):
PDF icon a2008no2p122.doc_.pdf
(downloads: 119)
  • 1843 reads