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

For citation:

Shabunin A. V., Akopov A. A., Astakhov V. V., Vadivasova T. E. Running waves in a discrete anharmonic self-oscillating medium. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 4, pp. 37-55. DOI: 10.18500/0869-6632-2005-13-4-37-55

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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2005-13-4-37-55

Running waves in a discrete anharmonic self-oscillating medium

Autors: 
Shabunin Aleksej Vladimirovich, Saratov State University
Akopov Artem Aleksandrovich, Saratov State University
Astakhov Vladimir Vladimirovich, Yuri Gagarin State Technical University of Saratov
Vadivasova Tatjana Evgenevna, Saratov State University
Abstract: 

The work is devoted to investigation of dynamics of running waves in the ring of Van-der-Pol oscillators with diffusive coupling. Regions of existence and stability are built in the parameters space. Typicalness of appearance of regimes with different wavelengths and regularities of their disappearance are considered. Influence of anharmonicity on multistability of spatio-periodic regimes is studied.

Key words: 
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Reference: 
  1. Kuramoto Y. Chemical Oscillations Waves, and Turbulence. Berlin: Springer; 1984. 158 p. DOI: 10.1007/978-3-642-69689-3.
  2. Cross MG, Hohenberg PC. Pattern formation outside of equilibrium. Rev. Mod. Phys. 1993;65(3):851–1112. DOI: 10.1103/RevModPhys.65.851.
  3. Parygin VN. Mutual synchronization of three coupled self-oscillating generators in the case of weak coupling. Radio Engineering and Electronics. 1956;1(2):197–204 (in Russian).
  4. Malafeev VM, Polyakova MS, Romanovskii YM. On the locking process in a chain of self-excited oscillators which are coupled via a conductivity. Radiophys. Quantum Electron. 1970;13(6):738–741. DOI: 10.1007/BF01030781.
  5. Mynbaev DK, Shilenkov MI. Mutual phase synchronization of generators connected in a ring circuit. Radio Engineering and Electronic Physics. 1981;26(2):361–370 (in Russian).
  6. Mal'tsev AA, Silaev AM. Operating modes of a chain of self-excited oscillators with “hard” limit cycles, linked, by reactive elements. Radiophys. Quantum Electron. 1979;22(7):573–579. DOI: 10.1007/BF01033562.
  7. Dvornikov AA, Utkin GM, Chukov AM. Mutual synchronization of a chain of resistance-coupled self-excited oscillators. Radiophys. Quantum Electron. 1984;27(11)967–972. DOI: 10.1007/BF01037390.
  8. Ermentrout GB. The behavior of rings of coupled oscillators. J. Math. Biol. 1985;23(1):55–74. DOI: 10.1007/bf00276558.
  9. Ermentrout GB. Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators. SIAM J. Appl. Math. 1992;52(6):1665–1687. DOI: 10.1137/0152096.
  10. Ren L, Ermentrout GB. Phase locking in chains of multiple-coupled oscillators. Physica D. 2000;143(1–4):56–73. DOI: 10.1016/S0167-2789(00)00096-8.
  11. Nekorkin VI, Makarov VA, Velarde MG. Spatial disorder and waves in a ring chain of bistable oscillators. Int. J. Bifurcat. Chaos. 1996;6(10):1845–1858. DOI: 10.1142/S0218127496001181.
  12. Daido H. Strange waves in coupled-oscillator arrays: Mapping approach. Phys. Rev. Lett. 1997;78(9):1683–1686. DOI: 10.1103/PhysRevLett.78.1683.
  13. Gurtovnik AS, Neimark YI. Synchronisms in the system of cyclically weakly coupled oscillators. In: Dynamical Systems: Interuniversity Collection of Scientific Papers. Nizhny Novgorod: Nizhny Novgorod University Publishing; 1991. P. 84–97 (in Russian).
  14. Garcia-Ojalvo J, Lacasta AM, Sagues F, Sancho JM. Noise-sustained signal propagation. Europhys. Lett. 2000;50(4):427–433. DOI: 10.1209/epl/i2000-00287-1.
  15. Sancho JM, Garcia-Ojalvo J. Noise-Induced Order in Extended Systems: A Tutorial. In: Freund JA, Pöschel T, editors. Stochastic Processes in Physics, Chemistry, and Biology. Berlin: Springer; 2000. P. 235–246. DOI: 10.1007/3-540-45396-2_22.
  16. Khovanov IA, Luchinsky DG, Mannella R, McClintock PVE. Fluctuations and the energy-optimal control of chaos. Phys. Rev. Lett. 2000;85(10):2100–2103. DOI: 10.1103/PhysRevLett.85.2100.
  17. Luchinsky DG, Beri S, Mannella R, McClintock PVE, Khovanov IA. Optimal fluctuations and the control of chaos. Int. J. Bifurcat. Chaos. 2002;12(3):583–604. DOI: 10.1142/S0218127402004528.
  18. Nekorkin VI, Makarov VA. Spatial chaos in a chain of coupled bistable oscillators. Phys. Rev. Lett. 1995;74(24):4819–4822. DOI: 10.1103/physrevlett.74.4819.
Received: 
27.01.2005
Accepted: 
29.07.2005
Published: 
30.11.2005
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