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


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Makarov V. A., Nekorkin V. I. Cluster synchronization in a chain of bistable self-exited elements. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 2, pp. 15-27. DOI: 10.18500/0869-6632-1998-6-2-15-27

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Russian
Article type: 
Article
UDC: 
621.373.1

Cluster synchronization in a chain of bistable self-exited elements

Autors: 
Makarov Valerij Anatolevich, Lobachevsky State University of Nizhny Novgorod
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

The phenomenon of synchronization of oscillations in а chain of bistable oscillators is investigated. It is revealed that the mutual synchronization of oscillations occurs to formation of phase or frequency clusters. The connection between sites of clusters in the chain and spatial dynamics of the system is discussed.

Key words: 
Reference: 
  1. Afraimovich VS, Nekorkin VI, Osipov GV, Shalfeev VD. Stability, Structures and Chaos in Non-linear Synchronization Networks. Gorky: Institute of Applied Physics AS USSR Press; 1989. 253 p. (in Russian).
  2. Loginov AS, Rzhanov AG, Elenskii VG. Multi-element semiconductor lasers. Telecommunications and Radio Engineering. 1986;8:49-64. (in Russian).
  3. Rарреl WJ. Dynamics of а globally coupled laser model. Phys. Rev. E. 1994;49(4):2750-2755. DOI: 10.1103/physreve.49.2750.
  4. Watanabe S, van der Zant HSJ, Strogatz SH, Orlando TP. Dynamics оf circular arrays оf josephson junctions and thе discrete sine—Gordon equation. Physica D. 1996;97(4):429-470. DOI: 10.1016/0167-2789(96)00083-8.
  5. Borisyuk GN, Borisyuk RN, Kazanovich YaB, Luzyanina TB, Turova TS, Tsymbalyuk GS. Oscillator neural networks. Mathematics and applications. Mathematical Models and Computer Simulations. 1992;4(1):3-43. (in Russian).
  6. Abatbanel HDI, Rabinovich MI, Selverston А, Bazhenov MV, Huerta R, Sushchik MM, Rubchinskii LL. Synchronisation in neural networks. Phys. Usp. 1996;39(4):337-362. DOI: 10.1070/pu1996v039n04abeh000141.
  7. Madan RN, editor. Chua’s circuit: А paradigm for chaos. World Scientific Series оn Nonlinear Science Series В. Vol. 1. Singapure: World Scientific; 1993. 1088 p. DOI: 10.1142/1997.
  8. Romanovskii YuM, Stepanova NV, Chernavskii DS. Mathematical Modeling in Biophysics. M.: Nauka; 1975. 343 p. (in Russian).
  9. Ermentrout GB, Kopell N. Frequency plateaus in а chain оf weakly coupled oscillators, I. SIАМ J. Math. Anal. 1984;15(2):215-237. DOI: 10.1137/0515019.
  10. Ermentrout GB. Synchronization in а pool оf mutually coupled oscillators with random frequencies. J. Math. Biology. 1985;22:1-9. DOI: 10.1007/BF00276542.
  11. Tass Р, Haken H. Sinchronization in networks of limit cycle oscillators. Z. Phys. В. 1996;100:303-320. DOI: 10.1007/s002570050126.
  12. Makarov VA, Nekorkin VI. Spatial-time dynamics of the chain of self-oscillating elements. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(2):3-9. (in Russian).
  13. Nekorkin VI, Kazantsev VB, Velarde MG. Dynamic copying in multilayer bistable gratings. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(5):56-68. (in Russian).
  14. Tass Р. Phase and frequency shifts in а population оf phase oscillators. Phys. Rev. Е. 1997;56(2):2043-2060. DOI: 10.1103/PhysRevE.56.2043.
  15. Golomb D, Hansel D, Shraiman B, Sompolinsky H. Clustering in globally coupled phase oscillators. Phys. Rev. А. 1992;45(6):3516-3530. DOI: 10.1103/physreva.45.3516.
  16. Mackay RS, Sepulchre J—A. Multistability in networks оf weakly coupled bistable units. Physica D. 1995;82(3):243-254. DOI: 10.1016/0167-2789(94)00243-J.
  17. Nekorkin VI, Makarov VA. Spatial chaos in а chain of coupled bistable oscillators. Phys. Rev. Lett. 1995;74(24):4819-4822. DOI: 10.1103/PhysRevLett.74.4819.
  18. Nekorkin VI, Makarov VA, Kazantsev VB, Velarde MG. Spatial disorder and pattern formation in lattices оf coupled bistable elements. Physica D. 1997;100(3-4):330-342. DOI: 10.1016/s0167-2789(96)00202-3.
  19. Makarov VA. Phase clusters in a chain of bistable oscillators with local connections. In: Yakimov AV, editor. Modern problems of radiophysics. Nizhny Novgorod: Nizhny Novgorod University Publishing; 1996. С. 94-99. (in Russian).
Received: 
16.01.1998
Accepted: 
01.04.1998
Published: 
08.07.1998